Do the following: Find the partial derivatives of the following functions:

a)

b)

c)

d)

e)

f)

g)

h)

i)

These are baby steps required to learn the techniques of solving differential equations.

Regards,

Nalin Pithwa

Mathematics demystified

October 16, 2020 – 1:14 pm

Do the following: Find the partial derivatives of the following functions:

a)

b)

c)

d)

e)

f)

g)

h)

i)

These are baby steps required to learn the techniques of solving differential equations.

Regards,

Nalin Pithwa

October 10, 2020 – 12:34 pm

Problem 1:

Evaluate:

Problem 2:

Evaluate:

Problem 3:

Evaluate:

Problem 4:

Evaluate:

Problem 5:

Evaluate:

Problem 6:

Evaluate:

Problem 7:

Evaluate:

Problem 8:

Evaluate:

Problem 9:

Evaluate:

Problem 10:

Evaluate:

Problem 11:

Evaluate:

Problem 12:

Evaluate:

Problem 13:

Evaluate:

Problem 14:

Evaluate:

Problem 15:

Evaluate:

Problem 16:

Evaluate:

Problem 17:

Evaluate:

Problem 18:

Evaluate:

Problem 19:

Evaluate:

Problem 20:

Evaluate:

Problem 21:

Evaluate:

Problem 22:

Evaluate:

Problem 23:

Evaluate:

Problem 24:

Evaluate:

Problem 25:

Evaluate:

Problem 26:

Evaluate:

Problem 27:

Evaluate:

Problem 28:

Evaluate:

There is one of the four possible answers:

(i)

(ii)

(iii)

(iv)

Problem 29:

The values of A and B for f(x) to be continuous at where

when

when x=0 are

(i) (ii) (iii) (iv)

Problem 30:

If when

and when

Find the value of k for which f(x) is continuous at .

Regards,

Nalin Pithwa

October 10, 2020 – 8:30 am

Problem 1:

Find the value of the following limit:

Problem 2:

Find the value of the following limit:

Problem 3:

Find the value of the following limit:

Problem 4:

Find the value of the following limit:

Problem 5:

Find the value of the following limit:

Problem 6:

Find the value of the following limit:

Problem 7:

Find the following limit: where

Problem 8:

Evaluate: , where

Problem 9:

Evaluate:

Problem 10:

Evaluate:

Problem 11:

Evaluate:

Problem 12:

Evaluate:

Problem 13:

Evaluate:

Problem 14:

Evaluate:

Problem 15:

Evaluate:

Problem 16:

Evaluate:

Problem 17:

Evaluate:

Problem 18:

Evaluate:

Problem 19:

Evaluate:

Problem 20:

Evaluate:

Problem 21:

Evaluate:

Problem 22:

Evaluate:

Problem 23:

Evaluate:

Problem 24:

Evaluate:

Problem 25:

Evaluate:

Problem 26:

Evaluate:

Problem 27:

Evaluate:

Problem 28:

Evaluate:

Problem 29:

Evaluate:

Problem 30:

Evaluate :

Problem 31:

Evaluate:

Problem 32:

Evaluate:

Problem 33:

Evaluate:

Problem 34:

Evaluate:

Problem 35:

Evaluate:

Problem 36:

Evaluate:

Problem 37:

Evaluate: . Then, (i) (ii) (iii) (iv)

Problem 38:

Evaluate:

Problem 39:

Evaluate:

Problem 40:

Evaluate:

Problem 41:

Evaluate:

Problem 42:

Evaluate:

Problem 43:

Evaluate:

Problem 44:

Evaluate:

Problem 45:

Evaluate:

Problem 46:

Evaluate:

Problem 47:

Evaluate:

Problem 48:

Evaluate:

Problem 49:

Evaluate:

Problem 50:

Evaluate:

Regards,

Nalin Pithwa

October 10, 2020 – 4:05 am

Problem 1:

Find the value of the following limit:

Problem 2:

Find the value of the following limit:

Problem 3:

Find the value of the following limit:

. Choose one of the following: (i) (ii) (iii) a(a\cos{a} + 2 \sin{a}) (iv)

Problem 4:

Find the value of the following limit:

Problem 5:

Find the value of the following limit:

Problem 6:

Find the value of the following limit:

Problem 7:

Find the value of the following limit:

Problem 8:

Find the value of the following limit:

Problem 9:

Find the value of the following limit:

Problem 10:

Find the value of the following limit:

Problem 11:

Find the value of the following limit:

Problem 12:

Find the value of the following limit:

Problem 13:

Find the value of the following limit:

Problem 14:

Find the value of the following limit:

Problem 15:

If the value of the following limit is -1, then find the value of a:

Problem 16:

Find the value of the following limit:

Problem 17:

Find if f(x) is given as follows:

Problem 18:

If , then is equal to (i) (ii) (iii) (iv) ab

Problem 19:

Evaluate the following limit:

Problem 20:

The function f is defined by :

in the interval

In order for this function to be continuous in , we have to define (a) (b) (c) (d)

Problem 21:

The function when and , (a) has removable discontinuity at (b) has irremovable discontinuity at (c) is continuous at (d) exists.

Problem 22:

Let be defined by

if

, if

If and are continuous in , then the value of b is (i) (ii) (iii) (iv)

Problem 23:

If , where , then is (a) 7 (b) 8 (c) 9 (d) 10

Problem 24:

If and then is (a) (b) (c) (d)

Regards,

Nalin Pithwa

October 10, 2020 – 3:16 am

Problem 1:

Find the value of the following limit:

Problem 2:

Find the values of the constant a and b such that the following limit is zero:

Problem 3:

Find the value of the following limit:

Problem 4:

If a, b, c, d are positive, then find the value of the following limit:

Problem 5:

Find the value of the following limit:

Problem 6:

Find the value of the following limit:

Problem 7:

Find the value of the following limit:

Problem 8:

Find the value of the following limit:

Problem 9:

Find the value of f(0) such that the following function is continuous at zero:

Problem 10:

Let be continuous at zero and . Then, find the numerical value of the following limit:

Problem 11:

Find the value of the following limit:

Problem 12:

Find the values of x where the following function is discontinuous:

Problem 13:

The value of p for which the following function may be continuous at zero is what:

, when , and

, when .

Problem 14:

Find the value of the following limit:

Problem 15:

If and , and , then the equation whose roots are is (a) (b) (c) (d)

Problem 16:

Find the value of the following limit:

Problem 17:

Find the value of the following limit:

Problem 18:

Find the value of the following limit:

Regards,

Nalin Pithwa

October 10, 2020 – 2:43 am

Problem 1:

If are the two roots of the quadratic equation , then the find the value of the following limit:

Problem 2: Given the following functio; find the value of f(0) so that the function is continuous at zero:

when .

Problem 3:

Find the value of the following limit:

Problem 4:

If , which numerical value divides ?

Problem 5:

Find the value of the following limit:

Problem 6:

Find the value of the following limit:

Problem 7:

Let it be given that and then find the value of the following limit:

Problem 8:

Find the value of the following limit:

Problem 9:

Find the value of the following limit:

Problem 10:

Find the value of b such that the following function is continuous at every point of its domain:

, when , and , when .

Problem 11:

Find the value of the following limit:

Problem 12:

Find the value of the following limit:

Problem 13:

Consider the following: . Then, which of the following is true (a) limit exists and is equal to (b) exists and it equals (c) limit does not exist because (d) limit does not exist because left hand limit is not equal to right hand limit

Problem 14:

Find the value of the following limit:

Problem 15:

Find the value of p given the following:

Problem 16:

The number of points of discontinuity of the function is (a) zero (b) 1 (c) 2 (d) 3

Problem 17:

Find the value of the following limit:

Problem 18:

Find the value of the following limit:

Regards,

Nalin Pithwa

October 9, 2020 – 6:54 pm

Problem 1:

Find the following limit:

Problem 2:

Let the given function be continuous in the interval . Then what must be the value of p?

, when

, when .

Problem 3:

Let the given function be continuous for , then find the most suitable values for a and b:

, for

, for

, for

Problem 4:

Find the value of the following:

Problem 5:

The function is not defined at . The value of so that f(x) becomes continuous at is (a) 1 (b) 2 (c) 0 (d) none

Problem 6:

Find the value of the following limit:

Problem 7:

Let the given function be . Find the value which should be assigned to f at so that f is continuous everywhere on the reals.

Problem 8:

Let it be given that and , x is not zero. What value of f(0) will make the function f continuous on the reals.

Problem 9:

Find the value of the following limit:

Problem 10:

If and , then the find the limiting value of as :

Problem 11:

Let it be given that . Then, the find the value of the following limit:

Problem 12:

Let it be given that when x is not zero and , when x is zero. Then, find the value of the following limit:

.

Problem 13:

Find the value of the following limit:

Problem 14:

Let it be given that when and , when is continuous at . Then, find the value of A.

Regards,

Nalin Pithwa

September 27, 2020 – 6:48 am

Problem 1: Find .

Problem 2: If , then what is the value of ?

Problem 3: If , then find the value of

Problem 4: Find the value of

Problem 5: Find the value of

Problem 6: Find the value of

Problem 7: Find the value of

Problem 8: If , what is the relationship between m and n if

Problem 9: Find

Problem 10: Find the value of a given the following:

when x less than or equal to -2.

when x greater than -2.

given that exists.

Problem 11: Let , then find the value of

Problem 12: Let then find the value of

Problem 13: The function is not defined when x is zero. In order to make this function continuous at zero, what should be the value of f at zero?

Problem 14: If the function given below is continuous at x=3, find the value of c:

for

for

for

Problem 15: If , when and , when when , then which of the following is true ? (a) f(x) is continuous at (b) (c) f(x) is discontinuous at (d) none of these.

Problem 16:

If , when x is not zero, and . If is continuous at , then find the value of .

Problem 17:

Let where and , then which value of will make f(x) continuous at

Regards,

Nalin Pithwa

September 26, 2020 – 12:57 pm

Problem 1: Which of the following is an indeterminate form ? (a) (b) (c) (d)

Problem 2: Which of the following is not an indeterminate form ? (a) (b) (c) (d)

Problem 3: If and exists then which of the following conditions is not always correct ? (i) (ii) (iii) (iv)

Problem 4: If exists, then (i) both and must exist (ii) need not exist but exists. (iii) neither nor may exist (d) exists but need not exist.

Problem 5: and then the function (i) is continuous at (ii) is not continuous at (iii) has a limit when but (iv) has a limit equal to when

Problem 6: If and then the function (i) is continuous at (ii) does not have a limit at (iii) has a limit when and it is equal to l.m (iv) has a limit when but it is not equal to l.m

Problem 7: Find

Problem 8: Find .

Problem 9: Find

Problem 10: Find .

Problem 11: Find

Problem 12: Find

Problem 13: Find

Problem 14: Find

Problem 15: Find

Problem 16: Find x if

Regards,

Nalin Pithwa