f(x) 3. What does lim = 0 show? X→∞ g(x) O g(x) grows faster than f(x) as x goes to infinity. Of(x) and g(x) grow at the same rate as x goes to infinity. O f(x) grows faster than g(x) as x goes to infinity. O L'Hôpital's Rule must be used to determine the true limit value.

Q: Give an example of two differentiable functions f(x) and g(x) such that: lim, 00 f(x) = lim, 0 9(x)…

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Q: 3. Sketch a graph of a function y = f(x) that satisfies all of the following (if possible): а. x-0-…

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Q: Let f(z) 2 = = (-)². Show that lim f(z) does not exist. z➡0

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Q: How do you find the limit of f(x) of the attached equation?

A: Notice that the graph is discontinuous at x=3.

Q: 1.Find f'(x) using the limit definition of f'(x)= lim (x+h)- f(x) for the following function: f(x) =…

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Q: . Let (x2 + 1 f(x) = 1( - 2)² if x> 1 if x<1 (a) Find lim,-I- f(x) and lim,→* f(x). (b) Does lim ,1…

A: Given: For (a),     limx→1- f(x)=limx→1 x2+1=12+1=2 and     limx→1+ f(x)=limx→1 x-22=(-1)2 =1

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: 3 - – If lim f(x) = 3.5 and lim,-2+ f(x) = 6. 5 , the function has a double sided %3D x→2- limit or…

A: Given,          limx→2-fx=3.5 and limx→2+fx=6.5We know that,           Condition of double sided…

Q: If f(x) = 5x² , then f' (x) = lim¬0 5(x+h)? –52? h True False

A: Given, If  fx = 5x2  ,  then  f'x = limh→05x+h2 - 5x2h We have to check the truthfullness of the…

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: Let F(x) = | 3e“ dt. Find lim F(x) if it exists. If the limit does not exist, explain why. x→0

A: see below the answer

Q: Let lim f(x)=4. Find lim (- 5') x→10 x→10

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Q: 4 - 3 + – Find the limit of f(x) = as x approaches o and as x approaches - ∞o. 9. 9 - X

A: Find the limit of the function .

Q: Find the limit of the function along the path y = 2x X-1 lim (x.y)-(0,0) y -1

A: We have to find the limit of the function along the path