I obtained f'(x) by finding lim[f(x + h) – f(x)] and Jimh, and then using the quotient rule for limits.

Q: Suppose that lim (x,y)→(3,1) f(x,y) = 6. What can you say about the value of f (3,1)? What if f is…

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Q: Evaluate the limit.

A: The limit of a function limx→Xfx=Y means that value of  function fx can be as close to Y by making…

Q: Find the limit, if it exists.

A: Here given as

Q: 2. x- 4 lim tan(rx)

A:

Q: Find the limit. -5x cos(x) lim

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Q: Find the limit. sin(2x) lim

A: To determine the value of the limit.

Q: Find the limit. lim etan x x-(1/2)+

A: 0 is answer

Q: Find the limit. lim sech(x) X -0

A: To find limit: limx→-∞sechx Solution: We know that sechx=2ex+e-x Therefore,…

Q: Find lim (2+x)" * using L'Hôpital's rule. 1/x

A: Given the given expression is limx→∞2+x1x.

Q: Evaluate the limit: sin(5x) cos(6x). lim x→0

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Q: Evaluate the limit using L'Hôpital's rule. limx→0  ex+2x−1/9x

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Q: Evaluate the limit sin 9x lim x →0 sin 3x

A: We can solve the problems by finding the value of the function at  the given limit.

Q: Evaluate the limit: sinx lim x→0 e4x – 1

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Q: Find the limit.

A: Given- x→lim0 sin3xx To find- the value of the above limit. Formula used- Using the standard form as…

Q: Evaluate the limit. lim     In (Sinh x)x →0+

A: we have to evaluate the limit. lim     In (Sinh x)x →0+

Q: Find the limit. sin(4x) lim 5x

A: Solution: The objective is to find the given limit

Q: Find lim f(x) and determine if continuous at x =2 エ→2

A: We have to check

Q: Find the limit. sin(2x) lim 3x

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Q: Evaluate the function f(x) = x / (√x + 1 − 1) at several x-values near 0 and use the results to…

A: To evaluate: limx→0xx+1-1 using value of function at several values of x near to 0. Solution: We…

Q: 2. If it exists, find lim f(x) where X--1 x =-1 f(x) = { *x– 1)³, x+-1 4, If the limit does not…

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Q: Find the limits limx→0+x-1/ln x

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Q: Evaluate the limit using L’Hôpital’s Rule.

A: Given: limx→0sin6x4x

Q: : Find the limit by using l'Hôpital's Rule. tan x sec 2x lim-o 3x

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Q: 2. Use L'Hospitaľ's Rule to find lim (1+ x)*

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Q: sin² x lim 0-x X

A: As per the company guidelines We can first question only. Please understand. Kindly repost the…

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: Find the value of the limit: lim x→0* sinx+ tan x

A: Given query is to find the value of the indicated limit

Q: Make a table of function evaluations near the limit and use this to estimate the value of the limi…

A: Given: f(x)=limx→0xsin)(x)

Q: Evaluate the limit with either L'Hôpital's Rule or previously learned methods. 8e3x 8 lim x-0 sin(x)

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Q: Evaluate the limit using L'Hospital's rule et – 1 lim x0 sin(4x)

A: we have given limit, we have to find it's value using L' Hospital rule. lim x→0ex -1sin 4x

Q: Find the limit.   Lim x→∞             (1+2x)5/2 ln x

A:

Q: sin 2x lim

A: Consider the given function, limx→∞sin2xx since is a continuous periodic function, as sin2x∈-1,1. as…

Q: Find the limits limx→0+x (ln x)2

A: Consider : limx→0+x(ln2x). Modify the limit function. limx→0+(ln2x)1x…

Q: Find the limit, if it exists.

A: First of all, use the limits property and apply the limits on numerator and denominator.

Q: Evaluate the limit using techniques from Chapters 2 and 4 and using L'Hôpital's Rule. sin(2x) lim 5x…

A: Limit: a)    x→0limsin (2x)5x=x→0limsin (2x)2x*52=25x→0limsin(2x)(2x)=25.1=25We know ,…

Q: Estimate the value of the limit lim, 40 COS x if it exists, by filling out this table and then…

A: We have to find the limit of the function and want to find some values to conclude graphically.

Q: Find the specified limit. f(x) - x+2, x > -1 lim f(x) ?

A: The given function is            f(x) = x2,  x<-1x+2, x>-1 We have to find the following…

Q: sin(2x) 1) lim

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Q: a) By graphing the function f(x)=(cos2x-cosx)/x2 and zooming in toward the point where the…

A: Graph: f(x)=cos(2x)-cos xx2f(x)=cos2x-sin2x-cos xx2

Q: find the limit lim as x approaches 0 from the right of (square root of x) / (ln (1+x))

A: We need to evaluate the given limit.limx→0+xln1+x

Q: We determined that l'Hospital's rule applies to the limit  lim x→5   x2 − 10x + 25 x2 − 5x

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Q: Evaluate the limit sin 2x lim z+0 9x

A: Answer and explanation is given below

Q: Use​ l'Hôpital's Rule to find the limit.   lim  x→0             x7x / 7x−1

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Q: Find the limit by interpreting the expression as an appropriate derivative. e2x lim- 1 i X0

A: As we already know that, dydxx=a=limh→0f(a+h)-f(a)h

Q: Evaluate the limit: sinh x2 – x2 lim x→0 sinhx − x

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Q: Compute the limit below. Justify your answer. sin(24x) lim- 39x

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Q: Use l’Hôpital’s rule to find the limits

A: Let the given limit be L - L = limx→0 x2lnsecxUsing L-hospital rule, differentiating numerator and…

Q: Find the limits using any appropriate method. ex-e-x-2x 4.4 #40 lim x-0 x-sinx

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Q: Find g'(x) for g(x)=-x^2+3x+2 by using the limit definition of a derivative.  lim x-->0…

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