1, , , then find .

Option (A)

Option (B)

Option (C)

Option (D)

Solution 1: Given that so that

and given that so that

and so we get so that correct choice is option A.

2. If and then find when

Option (A) 0

Option (B)

Option (C)

Option (D)

Solution 2:

which is equal to the following at

so that the correct choice is C.

3. If , then find

Option A:

Option B:

Option C:

Option D:

Solution 3:

Let where we put so now let

So, we get and and

So we get

So now

And,

Hence, we get the following:

Question 4: Find the following:

Option a:

Option b:

Option c:

Option d:

Solution 4:

Let

Let , , , and

so

Let

Let , and

Let

so that

so that so the option is a.

Question 5:

If then find .

Solution 5:

Question 6:

If , then is equal to

(a) 1/2 (b) 1/3 (c) 1/6 (d) 0

Solution 6:

Given that

Hence, we have

So, at x=0, on substitution we get .

Question 7:

If , , then find .

Solution 7:

Given , let so that

so that

Now, so that

so now

.

Question 8:

Find

Solution 8:

Let it be given that

Now, let us simplify this as where and

Now, first consider . Taking derivative of both sides w.r.t. x, we get

….A

Now, next consider . Takind derivative of both sides w.r.t. x, we get

….B

So that we get using A and B.

Question 9:

If , then find

Solution 9:

Given that

. Taking derivative of both sides w.r.t. x, we get

which is the required answer.

Question 10:

If , then find .

Solution 10:

Given that

Taking logarithm of both sides w.r.t. any arbitrary valid base,

so that

Taking derivative of both sides w.r.t. x, we get the following:

, so that finally we get the desired answer:

More later,

Cheers,

Nalin Pithwa