1 Calculate the difference quotient for f(x) = at a = 4. V2x + 9 (Express numbers in exact form. Use symbolic notation and fractions where needed.) f(4 + h) – f(4) h Calculate f' (4) by finding the following limit. f(4 + h) – f(4) lim h-0 (Give an exact answer. Use symbolic notation and fractions where needed.) f' (4) = Find an equation of the tangent line to f(x) at a = 4. (Express numbers in exact form. Use symbolic notation and fractions where needed.) y =

Q: 1. (a) Using the limit definition of the derivative only, find f'(x) where f(x) = x. If you use any…

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Q: Calculate each of the limits in Exercises

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A: To write that L-Hospital rule applies or not

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Q: 5 if x - 3 Calculate the following limits. Enter "DNE" if the limit does not exist. lim f(x) = I+…

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Q: 4. Show that In x lim x→1 x – 1 1. (Hint: Note that In In x-ln 1 x-1 and interpret the limit as a…

A: Given: To prove that limx→1 ln xx-1=1 using the limit as a derivativeFormula:…

Q: Q3 :(A): By using "L' Hopital rules"; Find the limits of : 1 (1) lim,-ol1-cos x sin2x (2) lim,…

A: 3)1) limx-0[1/(1-cosx) -2/sin2x ] 2) limx-0(tan-1x-x) /x3 Repost the next question.

Q: 5. Find the limit or show that it does not exist. sin(x – 1) lim 2 x→1 x´ + x -2

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Q: lim h--->0 (f(2+h)-f(2)) / h , where f(x)=4x+8

A: Given f(x)=4x+8 So f(2+h)=4(2+h)+8=4h+16 And f(2)=4(2)+8=16

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Q: Differentiate with respect to x y = e" cos(x²) e* (cos(x*) – 2x sin(x²)) e* cos(x²) – 2x sin(x²)…

A: y =excos(x2) dy/dx = excos(x2) -2xexsin(x2)           =ex(cos(x2) -2xsin(x2)) option 2 is right…

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A: Given,         limx→02sin23x3x2

Q: Q.1 Evaluate the limit x-3 sin2x 1) lim(2x2 +x + 1) 2) lim 2-9 3) lim x-1 x-3 x2-x+1 4) lim x+00…

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A: The given limit of the function:

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Q: Q1: Find the Limits of: Тan x 1- lim X+Sin x+VX 2- lim xo X+Sin x 3- lim vx2 + 1- Vx2-x

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Q: • If you are asked to find z- or yvalues, enter either a number or a list of numbers separated by…

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Q: 1. Find the derivative of f(x) = 2. at x = 0 using the definition of the derivative as a limit. Va +…

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Q: 8. Evaluate the limit by using a change of variable. x* - 1 Vx – 2 а. lim 8 x - 8 d. lim Vx – 2 27…

A: According to the L' Hopital rule, if the limit of a rational function, f(x)=N(x)D(x) , is to be…

Q: 1. lim (x+5x2 – 7x + 1) x-2 ( x +4 if x<-1 if – 1<x <1 if x 21 8. lim f(x), where f (x) =3 2x + 1…

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Q: B) Find the limits by using L.Hopital rule : x²–16 2. lim x→4 (Vx+5)-3

A: The function is a rule that associates or fixes a number to the particular point x. If , then the…

Q: Find x/2 x-3 lim 148 x+1 O limit does not exist e^-2 Oe^-4 0-2 O-4 O Other:

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Q: 1 if x – 2 Calculate the following limits. Enter "DNE" if the limit does not exist. lim f(x) = x -…

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Q: 1. lim x-> -7 f(x)=    2. lim x-> -3 f(x) =  3. lim x->-2- f(x)=

A: Note : As per the authoring guidelines,when multiple subparts are in one question,then only first…

Q: Calculate the limit for the function f(x) = Ex + 4 over the interval [0, 4]. Verify your answer by…

A: Given the function

Q: B) Find the limits by using L.Hopital rule: 7x 1. lim x-0 sin 2x x2-16 2. lim x-4 (Vx+5)-3

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Q: [In (x+1) Evaluate the limit of the function f(x) =er as x approaches 0 using Table of Values…

A: Consider the function  f(x)=ln(x+1)x To find the limit of the function as x approaches 0 using table…

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A: We have to find multiplication factor for given Limit.

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: compute lim as x goes to infinity of ln(x)^1/ln(x)

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Q: 2 – x x2 if x 5 - Calculate the following limits. Enter "DNE" if the limit does not exist. lim f(æ)…

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Q: B) Find the limits by using L.Hopital rule: 7x 1. lim X0 sin 2x x2-16 2. lim X+4 (VI+5)-3

A: *to find :- limits, using L-Hopital rule.

Q: 28. Use the limit definition, lim 7 (x+h)- f(x) to determine the derivative of x-1. [Value of 4] h0

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Q: 5. Find the limit or show that it does not exist. sin(x – 1) lim x→1 x´ +x –2 2

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Q: Q2.) Find the limit ( 1 lim X+x cos x 1. X→ 0 sin x cos x |x + 2| 2 - lim(x + 3) x-2 x + 2 lim sin…

A: solve using properties of limits

Q: 9 -x2 if x 1 .What value of c makes g(x) continuous at x = 1? Show all conclusions. 2 Vx-4 Using…

A: For a function to be continuos, the left hand limit should be equal to the right hand limit.…

Q: Q3: Choose A or B (one only) fx2 +2x x-6x if xs-2 if x>-2 A) Check the continuity of the function…

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Q: Q3 :(A): By using " L' Hopital rules "; Find the limits of: 1 (1) limx-o[: 1-cos x 2 sin²x (2)…

A: We have to find the limit using L Hospital rule.

Q: Q1- Evaluate the limit :- 1- lim - ( - cos) (1+ sin ) ) (1 + sin±)

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Q: S 2x² f(x) = 8 - x for x 2 Compute the left- and right-hand limits at x = 2 and determine whether ƒ…

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Q: Find the limit. lim x→4  sin(x − 4) x2 + 5x − 36

A: To Determine: find the limit of  limx→4sin(x-4)x2+5x-36 Given: welimx→4sin(x-4)x2+5x-36 Explanation:…

Q: Q3 :(A): By using "L' Hopital rules "; Find the limits of : (2) limx-o x-³ (tan-¹x - x)

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Q: 2) Use the definition of the derivative f(x+h)-f(x) lim hー→0 to find the derivative of f(x) =…

A: Our objective is to find the derivative using definition.

Q: 1) Use the definition of the derivative (which involves limits) to calculate g'(x) if g(x) = 3x² 5.…

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Q: x-3x+5 by X-0 4x2+2x+3 10. Find the limit: lim means of the L'Hopital Rule

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Q: exV – 1 Let g(x,y) (a, b) = (1,0). Show that lim g(x,y) does not exist. (x,V) - (a,b) %3D %3D x+y -…

A: Firstly it should be proved that limit does not exists and then recognize the two limit values so…

Q: 2. Evaluate the limit by Use the definition of the derviative to compute the derivative of f(x) = 1…

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Q: Q2.) Find the limit ( 10 lim 1- X- 0 X+ x cos x sin x cos x |x + 2| 2 - lim(x + 3) x-2 x + 2 lim sin…

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