Consider a function F (x) given by the following equation: F(x) = f(x)/g(x) where f(x) and g(x) are two functions such that limx→0 f(x) = limx→0 g(x) = 0. (a)  What rule do you need to get F′(x)? Write out and expression of F′(x) with respect to f and g.   (b) What rule do you need to get limx→0F(x)? Write out and expression of limx→0 F(x) with respect to f and g.   Find the derivative of f(x) = x^x^x Please show all your work and step by step.

Q: = (x),! %D (b) Use part (a) to find the derivative of f(x). 4 (X)d – (4 + x)f (a) Compute the…

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Q: How to use the standard y = f(x) notation to indicate that (a, b) is an element of the function f?

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Q: Let f(x) be the function f(x) 1. Find the following: x + 1 f(11) = f( – 10) | (4) 2 (-) f |

A: Given function is fx=xx+1-1. Put x=11 in the function. f11=1111+1-1=1112-1=-112 Therefore, f11=-112.

Q: Consider the function f(x) = x³ - 36x.

A: The objective of this question is to find the intervals on which the function f(x) = x^3 - 36x is…

Limits

When it comes to calculus, limits are considered to be a very important topic of discussion. The main importance of limit lies in expressing the value of a function as it gets closer to a certain value. Also, limits can help you to understand other topics, such as continuity and differentiability better. In a broader sense, every calculus notion is a limit. Other branches of calculus have also been derived from limits.