Let f(x) = sin(sin(sin.x)) for for all x in R (f(x) x-0 g (x), and g(x) = (sinx), VxER, then lim is ...

Q: 3. Let f(2) = if z + 2i, while f(2i) = 3+4i, is f(2) continuous at z = 2i? 2- 2i 4. Evaluate lim (az…

A: 3)Given:

Q: f(x) – f(c) If lim exists, it equals the slope of the х — с to the graph of f at the point (c,…

A: If    limx→cf(x)-f(c)x-c  exists;

Q: Let f(x) = x² + 3x – 2 f(x) – f(1) a) Find lim x- 1 x+ 1 b) Use your answer in part (a) to find an…

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Q: If f(x+ y)= f(x)f (y) for all x, y eR and f (x)=1+g(x)G(x), where lim g (x)=0 and lim G (x)…

A: The problem has been solved in detail in the next step.

Q: Let f and g be real functions. Show directly from the definitions that if f is everywhere continuous…

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Q: 3. Consider the function f(x), whose graph is shown below. Determine the limit of a function, by…

A: The limit exists at a point means that ..... LHL left-hand limit of the function should be equal to…

Q: Does limx → -1+ ƒ(x) = ƒ(-1)?

A: From the graph we see that at x=-1 there is a closed circle and the graph is right continuous at…

Q: Evaluate lim (x,y) →(0,0) x³ +35x² + 7y²2 5x² + y² 11

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Q: x² sin x (x, y) (0,0) x² + y² Determine whether lim exists.

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Q: Does limx →-1+ ƒ(x) exist?

A: x →-1+ means on the right side of x=-1 From the graph, we see that as the graph approaches -1 from…

Q: If f(x)=x2−9x−3 , what is limx→3+x2−9x−3 , limx→3−x2−9x−3, and f(3) ?   Is f(x) continuous at 3?

A: Given,              f(x) = x2 − 9x − 3

Q: 4. Let g(x)=x sin ¹(²) ₁ 0+ and define Prove that lim f(g(x)) does not exist. f(x) = 1, x 0 x=0

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Q: If f(x) = Vx² + x – x, find lim f (x), where f(x) is defined at X → 0.

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Q: The graph of f(x) passes through the point (4, 0). The slope of the line tangent to the graph at the…

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Q: 10. Let f(x) be a function such that f(0) 5, and lim fz)- = 4. Let g(x) = f(tan(rx)). Find g'(5).

A: The objective is to find g'(5).

Q: f(x, b) – f(a, b) fe(a, b) = lim x - a OTrue False

A: Given a limit : fxa,b=limx→a f(x,b)-f(a,b)x-a We need to find it it's true or false. Let's begin.

Q: Let f(x) = 9x² - 4x + 8. Determine f(a+h). Simplify completely. f(x+h) = Determine f(x+h)-f(x) h…

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Q: f(x+h. f'(x) using the definition lim h-0 O 26x + 30 O 5z + 13 O 5x O 10x + 13 O 10z

A: for the function f(x)=5x2+13x+30 find f'(x) using the definition limhf(x+h)-f(x)/h 26x+30 5x+13 5x…