The following limit represents the derivative of a functionf at a point a. 5 tan 6. V3 f '(a) = = lim %3D h→0

Q: The limit used to find the derivative is f(t) – f(x) dy dx lim definition %3D t- x

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

A: Plug x=4 to find f'(4) Answer: f'(a)= -1/16

Q: 1) Given f(x, y) = x derivative of f? which of the following is Əyox the mixed second order par f

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Q: Find the slope of the tangent line at a for the graph of the f(x) = xtan z y(x) be given implicitly…

A: a) Here we have to find the slope of the function f(x)=xtanx .......................... (1)  Let…

Q: Which of the following is the derivative of * f(x) = In(tanhz)? %3D

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

A: We need to evaluate an equivalent expression of the following derivative using limit definition…

Q: express the limit as a derivative.

A: Given limit is: The limit definition of a derivative is given by:

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: In the given equation as follows , determine whether the statement is true or false. If it is false,…

A: f is continuous function on [0,∞) and ∫0∞f(x)dx diverges

Q: Use the limit definition of the derivative to find the instantaneous rate of change of f(r) = V9r +…

A: Given:       fx=9x+5 at x=1  Instantaneous rate of change :    If y=fx, the instantaneous rate of…

Q: In Graphs: 8) Based on the graph of y = g(t) below, state the value of each limit if it exists. If…

A: Instantaneous rate of change is negative means tangent slope is negative.

Q: Defermine the derivative of the following functions using the long method (using limits). 1. y =t –…

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Q: Express the limit as a definite integral. lim 40 E xk A xk; [-5, 1] k=1 1 9x8 dx -5 x9 dx x9 dx x dx

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Q: Use the limit definition of the derivative to prove the following special case of the Quotient Rule:

A: We have to prove the following derivative by using limit definition: ddxfxx=x f'x-fxx2 We know for…

Q: Which of the following represents the slope of the tangent to f(x)=Vx+1 at x=8 ? Select one: 8+h-/8…

A: As we know that the expression for the slope of the tangent to the curve is:   limh→0fx+h-fxh…

Q: Express the limit as a definite integral. n 7 lim 8 1 + i = 1 n- o n dx

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Q: Hiwofind the derivative of the function fwith respect to Vaniable t,, tz when ti-l, tz=3 2. X=Lncti)

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Q: Express the limit as a derivative.

A: Given, limθ→πcos θ-sin θ+1θ-π

Q: Computing the derivative of ƒ(x) = x2 ex

A: Consider the given function fx=x2ex

Q: Find the derivative of f(x) at r = 0 using the definition of the derivative as a limit. %3D Va +I

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Q: Find the limit as x approaches c of the average rate of change of the following function from c to…

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Q: Express the limit as a derivative.

A: Our Aim is to evaluate the limit of the expression given below:-limt→πsin (t) cos (t)t-π-(i)

Q: Use the definition of the derivative (that is, f'(a) = lim sec(x) da to compute h+0

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Q: Which of following limits is the derivative of g(x) =5x at =2? 10 – 5h lim h 10 + 5h lim h>0 h 10 +…

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Q: . Use the forward-difference formula to approximate the derivative of f(x)= Inx at x, =1.9 using…

A: Forward Difference: For small values of h, the difference quotient can be used to approximate with…

Q: given f(x) = (2x+1)/(x+3), use the limit definition to find the tangent line to graph of f(x) at x=0

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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: Let f be the function with derivative given by f' (z) = sin z +I cOs z for 0 <z < 7. On which of the…

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Q: Suppose f is differentiable with continuous derivative on [a, b]. Show that lim f(x) sin(nx) dr = 0.

A: To prove the given limit

Q: Fill in the blank/s:

A: We have to fill in the blank.

Q: (b) y = tan x

A: Use limit method of derivative

Q: Find an equation of the tangent line to the graph of f(x) = | t cosh (t² – 1) dt tan-lt 1+In (x) at…

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Q: e* + e * — х2 — 2 lim —х sin?x – x2

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Q: The following limit represents the derivative of some function f at sor a. (1+h)" – 1 lim h >0

A: Limit derivative formula is  limh-&gt;0f(a+h)-f(a)h from the given limit we can see that f(x)=1…

Q: E. Set up the limit definition for finding the derivative of y = sin x.

A: Givne that  y=sinx  From the limit definition find the derivative of y=sinx

Q: verify that L’Hôpital’s Rule applies and evaluate the limit.

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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: 8) Based on the graph of y = g(t) below, state the value of each limit if it exists. If it does not…

A: Observing from the given graph we have

Q: Ay Find the derivative of the following using lim Ax-0 Ar %3D dx ala

A: Part (a) - y = 4x2-5x       ...........(1)Given that,dydx = limx→0 ∆y∆x We can write it as - dydx =…

Q: | sin(ln 0) d0

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Q: Find the derivative(dy/dx) of following function f(x) = Sin(2x) (x+1)? %3D

A: It is derivative problem.

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

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Q: Evaluate the following limits by constructing their respective table of values. 1- cos(3t) 4. lim 3t…

A: note: as per our company guidelines, we are supposed to answer 3 sub parts of a given question.…

Q: Find the derivative of the following function 1 F(x) ds Va 5+7s4 using the appropriate form of the…

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Q: Let y =sqrt(x + sqrt(8x + 1)). Using only the definition of rate of change in terms of limit,…

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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: F(x) = x · S, 2e' cos-lt dt at x = 1 In x

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Q: Does the existence and value of the limit of a function f(x) as x approaches a ever depend on what…

A: Yes, existence and value of the limit of a function f(x) as x approaches a depends on what happens…

Q: Choose the correct answer for the following limit S sin t3 dt lim X→0 2 x4 (A) 1

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