Exercises: Evaluate x2 – 1 - 1. lim 1- 2x 1 3 2x 2. lim x→2+ x – 2 х? — 4 - -

Q: Cos x-1 2- Show that lim = 0

A: We have to find the limit of the given expression. this can be done as follows:

Q: What is the maximum value of y = cos x. For -5 < x <? 1 2 O 1/2

A: Topic = Derivative

Q: Does the function f(x) = 5x − cos(x) + 4 have a root on [−π, 0]? Justify your answer.

A: Explained below

Q: Q4: A) solve: 1+rsin 1) lim y-0 1+xcos

A: Given: limy→01+xsin1x1+xcos1x

Q: x + tan x 2? — 5х — 14 - (а) lim x0 3x + 4x² (b) lim (Do not use L’Hospital rule in part(b)) x7- x2…

A: Using rules of limit's.

Q: Evaluate using the Squeeze Theorem

A:

Q: Along the path z= e find 2. lim (2,4)→(1,0) y-4zy 3x-y-3

A: Here, we have to reduce this limit to a limit in a single variable by using the equation of curve.…

Q: Show that lim (z,y)→(0,0) 4 z - Va² + y? V16 – x² – y? – 2²

A: Show thatlimx,y→0,0z-x2+y24-16-x2-y2-z2=0

Q: A. MCQS: I. LIMITS (2x+7x+6 3x2+5x-2. 1. lim-2 ( - 2. lim,-2 x+2 A.0 B. C.D. co A. 0 B. 4 C. 12 D.…

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Q: Evaluate: lim, 0 sin 2t t³ (t-1)²

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Q: Lim as h approaches 0=[5e^x - 5e^(x+h)]/[3h]=

A: Given:  limh→0 5ex-5ex+h3h   Basic concept: The definition of the first principle of the…

Q: 2 sin? x lim х-0 5x(1+сos x)

A: Let L=limx→ 02sin2x5x1+cosxlimx→ac·fx=c·limx→afxL=25limx→ 0sin2xx1+cosxPlug in the value…

Q: c) ) et 2. Aprēķināt robežas sinx-x a) lim X-0 b) lim X0 cos x-1'

A:

Q: Evaluate using the result of Exercise 54

A: Given: limh→0cos3h-1h2 we know that 1-cos2θ=2sin2θ…

Q: lim (- %3D x2 - 2sinx + 2x O 1 42

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Q: 3.lf limT(x--1) [(x^3+x^2-ax)] =1-a, then a= O a. 1. O b. 0. C. -1. O d. 1/2. 4-The equation…

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Q: Let h(x)

A: hx=x2,      x&lt;23,       x=22,       x&gt;2 Now, The left hand limit at x=2 is,…

Q: . Use the sandwich theorem sin x (a) lim Vx 400

A: The given expression is: limx→∞sin xx

Q: .2.4 lim (z,y)→(0,0) x² + y?

A: follow next step

Q: lim is x-0 X O A. 0 О в. 1 C. 8.

A: B. 1

Q: lim,- S(x), given S(x) = {7-4x, x<1 {x +2 x21 %3D

A:

Q: Find the limits in Exercise

A: limx22-1x

Q: O i using The( 3) uence Xm>is

A: First we have to show that Given sequence is monotonic and bounded then it is convergent

Q: (3) Evaluate lim -(1+sin(4))t dt

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Q: RNEK : lim X-0 - dt = ? 14 + 1

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Q: If lim | f(x)dx does not exist, b00 a then | f(x)dx diverges. a Select one: False True

A: True  Improper integral said to be convergent if the limit is finite and that limit is the value of…

Q: Evaluate: limt o sin 3t t5 (t-1)² using L'Hôpital's

A: Since you have asked multiple questions in a single request we would be answering only the first…

Q: lim (x,y)→(1,–1) eV3x²+4y?

A:

Q: Vx? +12 - 4 x²-5x +6 2x-5x +6 a- Lim cos x b- Lim c- Lim d- Lim x - 2 x'-8 3x -8 --

A: If in limit denominator and numerator forms 0 by 0 use L hospital rule

Q: )Use the Sandwich Theorem to show that lim cos x-1 =0. x2 Find f'(x) for f(x) = sec(vx2 + 1).

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Q: Which of the following is not correct? 4dx 4dx A Jo Jx(x+6) = lim o Vx(x+6) C+ .3 dx .3 dx B h…

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Q: Let f(2) = C, be the upper half eircle J2| = R in the counterclockwise direction with R>1, and /= ,…

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Q: Q3) Find: (1) lim, V1+cos 2x (2) lim-2 (x+ 2) 14-x2

A:

Q: Q 4. (a). Simplify the indicated limits on the following. (CLO-2: LOL 3x²+5 lim X→∞ x2+1 [sinx lim…

A: Q 4. (a) (i) The given expression is limx→∞3x2+5x2+1

Q: tan ( xy) :? lim (х.,у) -> (0,1) х-y+x 1 (e) (d) - (а) 0 (b) 2 (е) 1 4

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Q: f'(0) = Is f(1.5)>0? ('Yes on not) lim fCh-)-f(-)

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Q: lim (2,y)+(0,0) In(2 + x² + y?) x2 + y?

A: We have to solve given limit:

Q: V2x(x-1) 3. lim-1 Jx-1|

A: Given limit, limx→12xx-1x-1

Q: Evaluate the following limits.

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Q: Q27. The value of lim x-0 (1+x)5-e5x+sin x² x2 is? →

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Q: Solve z4-1 lim z→i z-i

A: The given expression is: limz→iz4-1z-i

Q: Show that lim (x,y) → (0,0) 12 √16x +9y¹ 4x²+3y does not exist. Please show a complete solution.

A:

Q: g lim y²+6y y¬T [/y+1-3y2 y+1-3y²

A: Using standard limit substitution

Q: 13x3sin(는)= 13 2.플) .3, lim %3D (x.y) → (1,-

A:

Q: B) f(x) = x+3 (-6, 6<x<1 Is f cont. at x-6?

A:

Q: e 3x limx→0

A: Ans :    we will use DL Hospital rule to solve this question.

Q: tan(ху) = ? .2. (х,у) >(0,1) х*y+x lim

A:

Q: Which of the following will make limx→c f(x) and f(c) equal? limx→2 : (x²+x-6) limx→–1 (x³ − 2x + 3)…

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Q: lim aVx + 3 – b = 1, x - 1 Score А. 4 E. 1 В. 2 С. 1 4 -IN-IA

A: We can make it easier for you.