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Learn Exercise 13.1 with Free Lessons & Tips

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Question 1:

Evaluate the Given limit:

Solution 1:

= $\left ( \pi -\frac{22}{7} \right )$

Comments

Tasneem

Question 2:

Evaluate the Given limit:

Solution 2:

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Shivam Sharma

Question 3:

Evaluate the Given limit:

Solution 3:

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Question 4:

Evaluate the Given limit:

Solution 4:

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Question 5:

Evaluate the Given limit:

Solution 5:

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Question 6:

Evaluate the Given limit:

Solution 6:

Put x + 1 = y so that y → 1 as x → 0.

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Shivam Sharma

Question 7:

Evaluate the Given limit:

Solution 7:

At x = 2, the value of the given rational function takes the form.

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Shivam Sharma

Question 8:

Evaluate the Given limit:

Solution 8:

At x = 2, the value of the given rational function takes the form.

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Question 9:

Evaluate the Given limit:

Solution 9:

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Question 10:

Evaluate the Given limit:

Solution 10:

At z = 1, the value of the given function takes the form.

Put so that z →1 as x → 1.

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Question 11:

Evaluate the Given limit:

Solution 11:

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Question 12:

Evaluate the Given limit:

Solution 12:

At x = –2, the value of the given function takes the form.

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Question 13:

Evaluate the Given limit:

Solution 13:

At x = 0, the value of the given function takes the form.

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Shivam Sharma

Question 14:

Evaluate the Given limit:

Solution 14:

At x = 0, the value of the given function takes the form.

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Question 15:

Evaluate the Given limit:

Solution 15:

It is seen that x → π ⇒ (π – x) → 0

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Question 16:

Evaluate the given limit:

Solution 16:

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Question 17:

Evaluate the Given limit:

Solution 17:

At x = 0, the value of the given function takes the form.

Now,

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Question 18:

Evaluate the Given limit:

Solution 18:

At x = 0, the value of the given function takes the form.

Now,

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Shivam Sharma

Question 19:

Evaluate the Given limit:

Solution 19:

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Shivam Sharma

Question 20:

Evaluate the Given limit:

Solution 20:

At x = 0, the value of the given function takes the form.

Now,

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Question 21:

Evaluate the Given limit:

Solution 21:

At x = 0, the value of the given function takes the form.

Now,

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Question 22:

Solution 22:

At, the value of the given function takes the form.

Now, put so that.

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Question 23:

Find f(x) andf(x), where f(x) =

Solution 23:

The given function is

f(x) =

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Question 24:

Find f(x), where f(x) =

Solution 24:

The given function is

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Question 25:

Evaluatef(x), where f(x) =

Solution 25:

The given function is

f(x) =

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Question 26:

Findf(x), where f(x) =

Solution 26:

The given function is

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Question 27:

Findf(x), where f(x) =

Solution 27:

The given function is f(x) =.

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Question 28:

Suppose f(x) = and iff(x) = f(1) what are possible values of a and b?

Solution 28:

The given function is

Thus, the respective possible values of a and b are 0 and 4.

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Question 29:

Letbe fixed real numbers and define a function

What isf(x)? For some computef(x).

Solution 29:

The given function is_.

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Question 30:

If f(x) =.

For what value (s) of a does f(x) exists?

Solution 30:

The given function is

When a < 0,

When a > 0

Thus, exists for all a ≠ 0.

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Question 31:

If the function f(x) satisfies, evaluate.

Solution 31:

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Question 32:

If. For what integers m and n does and exist?

Solution 32:

The given function is

Thus, exists if m = n.

Thus, exists for any integral value of m and n.

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Shivam Sharma

All Exercises - Chapter 13 - Limits and Derivatives

Exercise 13.1

Exercise 13.2

Miscellaneous Exercise 13

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Learn Exercise 13.1 with Free Lessons & Tips

All Exercises - Chapter 13 - Limits and Derivatives

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