Given f(x) = |2x – 2|. 1) At which points is f not differentiable? Prove your claim using the limit definition of the derivative. 2) Find the secant line to the graph of f over the interval [0, 2].

Q: Compute the right-hand and left-hand derivatives as limits to show that the functions are not…

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Q: Let f (x) = 2x2 − 3x − 5. Show that the secant line through (2, f (2)) and (2 + h, f (2 + h)) has…

A: We know that, the difference quotient given as m=fa+h-fah            ⋯⋯1 is the slope of the secant…

Q: Use the limit definition to compute f '(a) and find an equation of the tangent line. f (t) = t −…

A: We find f'(t) using the limit definition first

Q: 2. Let f(r) 3/r. (a) Using the limit definition, find f'(1). (b) Find the equation of the line that…

A: 2.Given f(x) = 3/x By Limit defination,  f'(x) =limh→0 [  f(x+h) - f(x) ]/h

Q: Let f (x) = xex . Use the limit definition to compute f'(0), and find the equation of the tangent…

A: Given: fx=xex We know that f'x=limh→0fx+h-fxh…

Q: The function f (x, y) = sin(xy)/xy is defined for xy ≠ 0.(a) Is it possible to extend the domain of…

A: conditions of function to be continuous: At each joining point the value of limit from both sides…

Q: compute f ' (a) using the limit definition and find an equation of the tangent line to the graph of…

A: Given f(x)=x2-x The limit definition for derivative of a function is given as: Using the above…

Q: find limit that represents the slope of the tangent line to the following function at x = 2 ? 2 f(x)…

A: Given function f(x)=24-3x To Find that represents the slope of the tangent line to the following at…

Q: Given f(x) = 4Va +5, find f' (x) using the limit definition of the derivative. %3D f'(1)=

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Q: Let f(x) = 2x2 - 3x - 5. Show that the secant line through (2, f(2)) and (2 + h, f (2 + h)) has…

A: Definition used -                   The slope of secant line -…

Q: Find the derivative of the following functions using the limit definition. 1. f(x) = x² + 5x – 4 %3D…

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Q: Fill in each blank so that the resulting statement is true.

A: We know that the derivative of f at x, denoted by f'x, is defined by limh→0fx+h-fxh provided that…

Q: If f(z) = V1+ 4z, find f'(1), using the definition of derivative. f'(1) is the limit as z1 of the…

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Q: Use the limit definition to compute f '(a) and find an equation of the tangent line.

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Q: Based on your work in part a, on what interval(s) is f(x) continuous?

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Q: use the limit definition to compute f'(a) and find an equation of the tangent line. f (x) = x3 + x,…

A: For a function f(x) the limit definition for derivative at x=a is f'(a)=limh→0f(a+h)-f(a)h. The…

Q: Given f(x) = 6 x + 1, find f'(x) using the limit definition of the derivative. f' (x)3D

A: Given, fx=6x+1 We have to find f'x using the limit definition of derivative.

Q: Given f(r) = 7T, find f'(1) using the limit definition of the derivative, f(r + h) - f(x) f'(x) =…

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Q: Use the limit definition to compute f '(a) and find an equation of the tangent line. f (x) = x3 + x,…

A: Anwer: f'(0)=1

Q: Use the limit definition to compute f' (a) and find an equation of the tangent line. f(t) = √(t2 +…

A: Consider the provided function, ft=t2+1    a=3 Find the limit by the definition to evaluate  f'a and…

Q: 2e What is the limit of the function f (x) = as x + xo ? 1-e

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Q: Use the limit definition to compute f 1 (a) and find an equation of the tangent line. f(x) = 2x 2 +…

A: Given:                fx=2x2+10x,     a=3 Find: f3+h and f3 f3+h=23+h2+103+h…

Q: In each case use the limit definition to compute f'(0), and then find the equation of the tangent…

A: Given: a fx=xex   b fx=x2ex

Q: if f(z) = V3+ 3z, find f'(3), using the definition of derivative f'(3) is the limit as z+ of the…

A: Given query is to find the derivative using definition.

Q: f(x, y) = e¬aY sin(x + y) (г, у) —> (1, -1). as

A: We will plug the limits in function to find limit of function

Q: Compute the right-hand and left-hand derivatives as limits to show thatthe functions in Exercise are…

A: Given figure is,

Q: Use the limit definition to compute f 1 (a) and find an equation of the tangent line. f (x) = x +…

A: For a function f(x) the limit definition for derivative at x=a is f'(a)=limh→0f(a+h)-f(a)h. For a…

Q: Use the limit definition of the derivative function to find 4 x . dz Which of the following sets up…

A: In the question we have to find the correct option.

Q: If f:R to {0,1} and I is an interval on which f has both values , the f has a discontinuity in I.…

A: Given that f has both 0 and 1 in its range.  This means there will be some x and y values for which…

Q: We can now evaluate this limit to conclude that the derivative is as follows. 1 a1/3 + a2/3) f '(a)…

A: We have to evaluate limit

Q: 2. Write the limit definition of f '(a) and use the definition to find the indicated derivatives.…

A: The objective is to write the limit definition of f'(a) and use the definition to find the indicated…

Q: Use the limit definition to compute f 1 (a) and find an equation of the tangent line. f (t) = 2…

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Q: dy -) using definition with limit of the following: dr 4. Find the differentiation (- y = /2x + 1.

A: We need to find the differentiation of y=2x+1 using the definition of limit. Now, according to the…

Q: Find the value of b such that the limit of the function f(x) = cot 2x)(sin bx) as x goes to zero…

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Q: . Use the limit definition of the derivative to show that if f(x) = +, then f'(c) = = very c e R,…

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Q: The following limit represents the derivative of a functionf at a point a. 5 tan 6. V3 f '(a) = =…

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Q: Assume that f(x) is everywhere continuous and it is given to you that f(x) + 8 lim x→2 x - 2 = -4 It…

A: Consider the given expression limx→2fx+8x-2=-4 Or, -4=limx→2fx+8x-2                            …1…

Q: Let f (x) = In(x + 2). Use the definition of the derivative and your now expanded knowledge of…

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Q: 7- Use the limit definition to compute f' (x) and find equation of the tangent line at r = 3. f (z)…

A: topic - derivative of a function using limits

Q: Use the limit definition to compute f '(a) and find an equation of the tangent line.

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Q: Compute the right-hand and left-hand derivatives as limits to show that the functions are not…

A: y=x,  y=1x  &  P1, 1. Left hand derivative is,…

Q: 4. Use the limit definition of the derivative to test whether the following function f(x), given by…

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Q: Use the limit definition to compute f '(a) and find an equation of the tangent line.

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Q: 1. Let f(r) 5r?. %3D (a) Using the limit definition, find f'(3). (b) Find the equation of the line…

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Q: Use the limit definition to compute f '(a) and find an equation of the tangent line. f (x) = x−1, a…

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Q: Let f(x)=√18 x. Compute f'(2) using the limit definition f'(2) = Find an equation of the tangent…

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Q: Let f (x) = xex . Use the limit definition to compute f ,(0), and find the equation of the tangent…

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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.