Question

For values of h very close to 0, which function best approximates (tan(x+5)-tan x) / h

Answer 1

Answer:

$sec^2(x)$

Step-by-step explanation:

• This just means, what is the derivative of tan(x)

Answer 2

The function that best approximates the given situation is sec²x.

We have to find

$\lim_{h \to\00} \frac{tan(x+h)-tan x}{h}$

Since the given expression reduces to 0/0 form when we apply the limits

So, let us apply the L'hospital rule

What is the L'hospital rule to find a limit?

L'Hospital's Rule tells us that if we have an indeterminate form 0/0 or ∞/∞ all we need to do is differentiate the numerator and differentiate the denominator and then take the limit.

So, after differentiating the numerator as well as the denominator of the given expression with respect to h we get

$\lim_{h \to\00} \frac{sec^2(x+h)-0}{1}$

$= lim_{h \to\00} \frac{sec^2(x+0)}{1}\\\\= sec^2x$

Therefore, the function that best approximates the given situation is sec²x.

To get more about limits visit:

https://brainly.com/question/23935467