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Learn Exercise 13.1 with Free Lessons & Tips

Evaluate the Given limit:

 = 

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Evaluate the Given limit:

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Evaluate the Given limit:

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Evaluate the Given limit:

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Evaluate the Given limit:

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Evaluate the Given limit:

Put x + 1 = y so that y → 1 as x → 0.

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Evaluate the Given limit:

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

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Evaluate the Given limit:

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

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Evaluate the Given limit:

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Evaluate the Given limit:

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

Put so that z →1 as x → 1.

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Evaluate the Given limit:

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Evaluate the Given limit:

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

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Evaluate the Given limit:

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

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Evaluate the Given limit:

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

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Evaluate the Given limit:

 

It is seen that x → π ⇒ (π – x) → 0

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Evaluate the given limit:

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Evaluate the Given limit:

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

Now,

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Evaluate the Given limit:

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

Now,

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Evaluate the Given limit:

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Evaluate the Given limit:

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

Now,

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Evaluate the Given limit:

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

Now,

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

Now, put  so that.

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

The given function is

f(x) =

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

The given function is

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Evaluatef(x), where f(x) =

The given function is

f(x) = 

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Findf(x), where f(x) =

The given function is

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Findf(x), where f(x) =

The given function is f(x) =.

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

The given function is

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

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Letbe fixed real numbers and define a function

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

The given function is.

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If f(x) =.

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

The given function is

When a < 0,

When a > 0

Thus,  exists for all a ≠ 0.

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If the function f(x) satisfies, evaluate.

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

The given function is

Thus,  exists if m = n.

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

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