Use L'Hospital's rule to determine the following limit. Use exact values. e1a – 1 4x lim x →0 sin(3x)

Q: Evaluate the limit using L 'Hospital's rule: lim x to 0 e^x -1/sin(12x)

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Q: The value of the limit lim is x-0 sin x а) 0 b) 1 1 c) d) ∞

A: Given options are wrong.  Limit will be e^(1/6).

Q: Find the indicated limits, noting L'Hôpital's Rule wherever it is used. lim (1-ª)* (constant a)

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Q: Find the following limit using two different approaches: sin 6x limr->0 4x

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Q: Find the following limits, using L'Hospital's Rule where appropriate. cos(mx)- cos(nx) (a) lim x-0

A: The objective of the question is find the limit.

Q: Find the value of the given limit. lim I 0 tan(4x) I

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Q: Find the value of the limit lim SINX X 0 2x 02x (a) 0 (b) 1 (c) 1/3 (d) 1/2 (e) 1/4

A: Here we have to find the limit of the function. In the first step use the property of the limit:

Q: For the function given by q (x)= x² + 2x+1, use the limit definition of the derivative to compute…

A: Definition of the Derivative:        The derivative of f(x)  with respect to x is the function f'(x)…

Q: Find the limit. lim e 3t i е j + Sin2 tan(5t) k) t 0

A: The given expression is,

Q: Use l'Hôpital's Rule to evaluate the limit. COS X lim -X- 3. 3. O A. -3 V3 O B. C. 2 O D. -/2 1.

A: We have to find limit As per guideline we have to solve one

Q: lim 4 sin(x + n) + 3

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Q: Determine whether the statement makes sense or does not make sense, and explain your reasoning.

A: The derivative of the function using the limits is obtained by the formula f'(x)=limh→0f(x+h)-f(x)h,…

Q: x cos(2x) (c) lim x-0 sin(-3x)

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Q: Determine the following limit, using o or - o when appropriate, or sta lim sec 0 01/2+ . ond GU in t…

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Q: C- The result of the following limit is lim 1-0 sin t² t f

A: limt→0sin t2t

Q: sin x – x (a) lim (b) lim (1+ x)/* 1/x

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

A: We have to find the limits of the function by L'Hospital's rule: limt→∞et+t2et-t If we limits are in…

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

A: Consider the given function fx=x2ex

Q: sin²t lim t3 t→0

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Q: Find the limit of the following functions: x²/3 +x=1 lim x-00 x2/3 + cos² x 1- cosx lim- x-0 sin2x

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Q: Find the limit, if it exists. (If an answer does not exist, enter DNE.) lim x to 0 (9x^2 - 6x / x)

A: We first factor the numerator

Q: C-The result of the following limit is sin t² lim 1-0

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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: Can we use L'Hospital's rule to find the following limit? 1- tan(x) lim ! cos((2 x) X-

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Q: Q3. Compute the following limits if they exist. 1 (d) lim x sin

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Q: Find the limit. (Hint: Let x = 1 / t and find the limit as t→0+.)

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Q: bx a (c) lim| 1+

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Q: lim h→0 (e) cos( 4 + h) - 1 h

A: To find the limit of following function

Q: Use l’Hospital’s rule where applicable to find the limit.

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

Q: (b) limx tan

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Q: Evaluate the​ limit, where a and b are constants with b≠0. lim x -0 sin ax/ sin bx

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Q: Use​ l'Hôpital's rule to find the limit of limθ→0     7 cosθ−7/2θ.

A: Given limit is in the 0/0 form so we can use the L'Hôpital's rule

Q: Find the indicated one-sided limits, if they exist. (If an answer does not exist, enter DNE.) if x 0…

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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: Find the limit, if it exists. (If an answer does not exist, enter DNE.) lim 5 sin(x)

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Q: Find the limits of the functions below a) limr-3 x* sin x b) lim,

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Q: Find the limit. -j + sin(5t) k) lim -6t sin?(t)

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Q: Find the limit. est - 1 lim t-0 sin(t)

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Q: Evaluate the limits of the following functions, and verify your answer. (6x+3y)sin(2x+y) 4x +4xy+ y…

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Q: Find the limit, if it exists.

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

Q: 1 lim \3 Vx + 9/

A: Rationalization of an expression is done to remove the radical expression from the term. For…

Q: Estimate the limit numerically if it exists. (If an answer does not exist, enter DNE.) lim x→+∞…

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

A: To find the limit, limt→0sin5t2t using l' Hopital's rule. Solution: The given limit is ,…

Q: (b) lim log1 r+2+ (x – 2)? sin(2x2 – 3x – 2),

A: solution:-limx→2+ log13x-22sin2x2-3x-2=limx→2+ -log3x-22sin2x2-3x-2=limx→2+…

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

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Q: Use l'Hôpital's Rule to find the following limit. 5 sin (x) - 5x lim 2x3

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Q: Find the limit. tan(12t) lim t-0 sin(4t)

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Q: 1-sin x 18. lim TL X- 2.

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