Determine if the function the following function is continuous 2x for x <4 a) Lim f(x) wbere f(x) = x +4 4x - 8 for x2 4 b) Find the second derivate (higher order derivative) of the following functions a. fex) = (4x'/3) – 2x' + 21 + e*+ In (x³)

Q: 1. Find the equation of the tangent line of f(x) at the given point. f (x) = 6x – x2, (1,5)…

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Q: 3. FIND THE DERIVATIVE BY THE LIMIT PROCESS OFf(x) = Vx+2.

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Q: 2. Use the definition = f'(x) = lim f(w)-f(x) to find the derivative of y = tan x. dx w-x

A: Let's take; w - x = h w = x + h As w approaches x; w-x = h →0   f'(x) = limh→0  [f(x+h) - f(x)]/(h)…

Q: Q1) A) Find the tangent equation for the function: f(x) = Vx² + 5 at =2 ? B) Find the limits by…

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Q: 10 at x + 4 x = 0 using the limit definition of the derivative. Find the derivative f' (0) of f(x) =

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Q: 5a) Using the formula man = lim+)=/G2 determine the derivative/ slope of tangent for h→0 the given…

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Q: -10 For f(x) = 2x-3 show that f'(x) = e using the limit definition of the derivative. ind the…

A: (a) f(x)=52x-3 f'(x)=limt→xf(t)-f(x)t-x        =limt→x52t-3-52x-3t-x…

Q: 4. Find an equation of the tangent line to the curve, f(x) definition of the derivative. (Don't use…

A: Given problem:- Find an equation of the tangent line to the curve, f(x) = 1/(x2 + 1) by using the…

Q: Find the derivative of ¤(x) at x = /3/2 where rsin-'(x) $(x) = eº tan 0 do. x2

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Q: Use the limit definition of the derivative (as demonstrated on the left) to compute the exact…

A: We have to compute f'(1) using the limit definition i.e. the derivative of the square root function…

Q: By using the limit definition to compute the derivative of f (x) = cos 3x, which rules we need for…

A: Option (IV) is correct. See the attachment

Q: 2.) Investigate the derivate of the function ƒ(2)=Imz by using definiton of derivative.

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Q: Find the derivative of f (x) = 2/x using the limit definition.

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Q: The limit cos(x) +1 lim x – 9T represents the derivative of some function f(x) at some number a.…

A: In the given question, f(x) is cos(x) and a is 9π

Q: All edges of a cube are expanding at a rate of 6 centimeters per second. How fast is the surface…

A: We have to solve above problem.

Q: x 0 entiable at x = 0.

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Q: 4. Consider the function f(x) = Vx – 1 (a) Use the limit definition of derivative to find f'(x)

A: Ans:- Consider the function f(x)=x-1(a) we have to use the limit definition of derivative to find…

Q: Find the derivative of the function by the limit process. h(s) = −2 (square root of x)

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Q: The limit cos(x) – 1 lim с — 4т represents the derivative of some function f (x) at some number a.…

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

Q: Use the limit definition to compute the derivative of the function f(x) = Vx + 16 at x = 1. (Use…

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Q: fx て (X)

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Q: Find the derivative of the function by the limit process. f(x) = x2 + x − 8

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Q: (d) VT tanr - 2 V lim /4 VT x(4x – 7) Hint: divide both parts of the fraction by VT x and represent…

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Q: Discuss the relationsh ip between the derivative dy/dx and(lim) with drawing if it is required

A: See the attachment

Q: Find the tangent line to the curve y = x^2 −5x + 11 at the point (1, 7). Use the limit definition of…

A: slope of the tangent line is m=dydx at (1,7)   By limit definition of…

Q: find the derivative of the function the limit process. by flx) %3D

A: Given f(x)=1x2We know that derivative of f(x) with respect to x is defined…

Q: By using the limit definition to compute the derivative of f (x) = cos 3x, which rules we need for…

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Q: Find (a) lim x--4- f(x), (b) lim f(x), and(c) lim f(x). X- -4+ x- -4 for x > -4 15) f(x) = ! x + 4…

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Q: Find the derivative by the limit process. f(x) = 10 – x2 %3D

A: We know that the derivative of a function fx is given by:f'x=limh→0fx+h-fxh

Q: Let f(x) = V6x. f(x) – f(a) Using the definition of derivative at a point, f'(a) = lim х — а enter…

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Q: 4. Find an equation of the tangent line to the curve, f(x) = definition of the derivative. (Don't…

A: On solving this we will get

Q: Find y' if y = 5x + 2 using the limit definition of derivative.

A: Given that  y=5x+2

Q: Find the derivative of the following functions using the long method (limits) y= tan x

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

Q: (b) y = tan x

A: Use limit method of derivative

Q: 3. FIND THE DERIVATIVE BY THE LIMIT PROCESS OFF (x) = Vx + 2.

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Q: what the derivative fxy er hin ction Sas)=x'tan)

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Q: Please provide on how you did it step  by step. Use one of the two limit definitions of the…

A: The given function is  f(x) = 7/x To find the derivative of the function by using definition at x =…

Q: Find f'(x) using the limit definition of derivative.

A: We have given,

Q: 1. Let f(x) =1. Using the limit definition of the derivative, find f'(x).

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Q: 8. For the function: 2 f(x) x +3' use the limit definition of the derivative to find f'(x).

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Q: 2. (a) Give the definition of the derivative f'(x) of the function f(x) in terms of a limit. (b) Use…

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Q: 2.Given f(x)=5Vx-1, find f'(x)using the limit definition of the derivative.

A: Given f(x)=5x-1

Q: f(x) = 3-x/2x+

A: First we have to find derivative of function at x =-1 by using given forumla-

Q: 1) Use the limit definition to find the derivative of the function f(x) = 6x – x². Then find all…

A: Using limits definition:f'(x) = limh→0 f(x+h) - f(x)hf(x) = 6x - x2f(x+h) = 6(x+h)- (x+h)2   = 6x +…

Q: 3 Find the derivative with gicapeet to X If f(0 = 0-7 The derivatie with reapeet to X If -7X is…

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Q: Calculate the derivative of f(x) = x² – 3 at a using the (limit) definition of derivatives, by…

A: Given function is We will calculate f'(a) by using definition of derivatives as follows.

Q: 2. (a) Demonstrate the method of the limit definition of derivative to find the derivative of f(x) =…

A: Limit of differentiation

Q: 2. Let x² sin () if x + 0 g(x) = if x = 0. Is g differentiable at 0? If so, find g'(0). Justify your…

A: Given: gx=x2 sin1x,       if x≠00,     if x=0 To Find: Is g differentiable at x=0? If so, to find…