4x 24. lim x→1/4 tan x

Q: Use the limit definition to compute f '(a) and find an equation of the tangent line.

A: Answer: f'(-2)=-1

Q: If V 16x <f(x)sx+4 for all positive x-values, then what is lim f(x)?

A:

Q: Find the limits x2/3 + x1 lim X00 x2/3 + cos?x

A: Given: The function is f(x)=x2/3+x-1x2/3+cos2x   To determine: limx→∞ x2/3+x-1x2/3+cos2x

Q: sin t lim + 2 t+0 t

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Q: If f(x, y) approaches 1 as (x, y) approaches (0, 0) along the path y = mx, where m is any real…

A: To check whether the given statement is true or false.

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: Find the limit. sinx cos 4x lim x-0 x + x cos 5x 4 A) 을 B) 0 530 C) D) Does not exist

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Q: 7 sin(T2) In (zº) q(z) = %3D What is lim q(x)? ncwor bolow:

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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: Consider the function f(x) = vx for xE R and 0 <x < 32. Prove that lim,-s f(x) = 4. %3D

A: Given: f(x)=x for x∈ℝ and 0&lt;x&lt;32 we have to prove that limx→16f(x)=4

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

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Q: Among the solutions of the 3rd order linear ODE y" – y" + y' – y = 8et, only one function satisfies…

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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: Evaluate the limit.

A: We have to evaluate the following limits- limh→0sin4h4h

Q: Find the limit. t2 j+ sin(7t) k sin2(t) -2t ¡ + lim t→0 e

A: We have to find the limit: limt→0e-2t i+t2sin2t j+sin(7t) k

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

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Q: Find the limits limx→q(ln x)1/x

A: Given,     limx→qln x1x

Q: Find the limit. O 75 π O O' O O I 00 D8 - 150 lim sin¹. 5 x X→ 0 ¹7x

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Q: Compute the limit 1 a2 1 - x2 lim xa x а - What can you say about the derivative of f(x) = ?

A: Given limit :

Q: Find the limit of the transcendental function. lim x → T/2 4 sin x

A: Definition of limits helps to find the limit of the given function. The value is said to be the…

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

A: Consider the given function fx=x2ex

Q: Question 2 5x limr→-0 g² + 10x – 1 c→-∞

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Q: In each case use the limit definition to compute f'(0), and then find the equation of the tangent…

A: Given: a fx=xex   b fx=x2ex

Q: Find the limit of the following. V3 sin 0 lim 0→t/3 3

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

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Q: It can be shown that lim be¯b = 0. Use this fact to compute S*xe* dx.

A: Given: ∫1∞xe-xdx

Q: Find the value of the limit lim sin 6 t t - 0 sin 4 t (a) 2 (b) 1.5 (c) 1.7 (d) 1.9 (e) 1.8

A: Recall the famous rule of limit:

Q: In(x - 1)2 | 26. lim x→2 In(3 In(x - 1)

A: L=limx→2ln(x-1)^2ln(x-1)

Q: Use the definitions of the hyperbolic function to find each of the following limits. lim x→∞…

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Q: Q1: (a) Find the limit of the following: x2+3 sin x 3) lim x0 ex-1 1-cosx 1) lim 2) lim ++zx 00+x X0…

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Q: Find the limit of the function along the x-axis xy lim (x.y)-(0,0) x2 + y?

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Q: Find the limits by rewriting the fractions first.

A: We have to find the limit: limx, y→0, 01-cosxyxy Rewriting the fraction using trigonometric formula,…

Q: If [ f(x)\dx<∞ show that limf(x)dx=0 k→∞00 1

A: We have to prove that given expression.

Q: 6ln (1+x) lim х>0 2е3х—2secx

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Q: Find the limit and discuss the continuity of the function. lim sin 1. (K. y)(27, 4) y lim 2. (x,…

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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: 1-cost lim sint et-1 + t t t+0

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Q: 1 lim x sin x x2 x→0 O 1/5 O 1/7 О 16

A: Given, limx→01x sinx-1x2

Q: 70. J, f(x) dx may not equal lim , f(x) dx Show that 2x dx o x² + 1 diverges and hence that 2x dx x²…

A:

Q: a)Express the limit as a definite integral. Σ (3c-5)Ax, xe[0,1] lim 2 b) and then evaluate it.

A: lim∆→0∑i=1n3c2i-5∆xi  x∈[0,1]∑ =∫∆xi=dx∫01(3x2-5)dxThis is definite integral

Q: Find the limit or prove that it does not exist lim (2,y)→(0,0) T° cos x + 2y sin y x2 + 4y2

A: We will evaluate the limit limx, y→0, 0x3cos x+2y3sin yx2+4y2  using polar coordinates.

Q: S (2t)*dt lim x→ =? х* — 1

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Q: 1. Show that for all f e L'(R) lim da = 0.

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Q: If x Vx sf(x)s -x+ 1for all positive x-values, then what is lim f(x)?

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Q: S, f(x) dr may not equal lim , f(x) dx. Show that 2x dx x* + 1 diverges and hence that 2x dx ? + 1…

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Q: Find the limit of (x3+x2)1/2sin(((2)1/2pi)/x) as x approaches 0

A: To find

Q: Find the limit by numerically. 1 lim 1+ It| 1 |t – 1| t-0

A: Limit is the value of the expression as the independent variable approaches certain value, not…

Q: Find the limit as x approaches infinity of the function V2 – x2 h(x) х3 — х + 1

A: Given:  h(x)=2-x2x3-x+1h(x)=x2 2x2-1x31x3-1x2+1  (Taking highest power of x in the…