ketch a graph of a function satisfying the following properties.  1) lim f(x)= -2 x--> 5 2) f'(5)=DNE

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A: This is the integration in the form of summation problem

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A: “Since you have asked multiple questions, we will solve the first question for you. If you want any…

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A: I have written the formula in the solution part with explanation

Q: 20 . Using the definition of derivative at a point, f'(9) f(x) – f(9) x – 9 Let f(x) lim enter %3D…

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A: By defining f(0)=1 the function f will be continuous at 0.

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A: To determine the slope of the line and equation of tangent line.

Q: 1- cos(x/6) lim II

A: Solve the limit

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Q: 2. Find limits numerically. Use at least 3 relevant x-values for each. sin(4x) sin(4x) (a) lim x→0-…

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A: This question is about finding derivative about a point .

Q: 1. How do I solve this?     2. How would I find the tangent line to the graph at x=-1

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A: Given that:

Q: For question 17 –18, find the limit. sin 4x lim x>0 x 17. sec x-1 lim 18.

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Q: 9. Sketch a graph that has the following properties: (i) ƒ is continuous on (-∞, ). (ii) f'(x) 0 on…

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Q: 02.) Find the limit lim X+x cos X sin x cos x 1- X→0 lim sin 5x SIn 4x 3-

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Q: 4. For what values of x does the graph of f have a horizontal tangent if f(x) = V3 x – 2 sin(x).

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Q: 3) Use L'Hopital's Rule to evaluate and check your answers numerically: (a) lim x→0+ (sina) 1 (b)…

A: Given: (a) limx→0+sin xx1x2            (b) limx→01sin2 x-1x2 To find: Evaluate using L'Hospital…

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Q: This limit represents the derivative of some function V16+h-2 f at some number a. State this f and…

A: Given limit as a derivative of the function limh→0(16+h)14-2h  we have to find the value of a and…

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Q: 3) Use L'Hopital's Rule to evaluate and check your answers numerically: sin x (a) lim x→0+ 1 1 (b)…

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Q: Q.NO.2: i. Find the limit Зх — sin(kx) lim - k + 0 ii. Find the relative extrema using both first…

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Q: 4x Consider the function f(x) : 3 – x a. Use the \underline{limit definition of derivative} to find…

A: We can solve all these points in the following way:-

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Q: Evaluate

A: Our Aim is to evaluate the limit given below:-limx→0tan (2x)x-(i)