28. Find the limit of the following. sine- /2 lim 0→n/4 e-4 sine-2 lim 0→1/4 0-

Q: Series 8ine) the limi t use to tany- y? cosy Siny limit

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Q: Compute the following limit: 1-cos 2z 1. lim I→0 z sin 2x· Hint: 1 – cost = 2 sin? t.

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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 the limit of the trigonometric function.

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Q: 1. Determine if the following limits exist: x² + y5 lim (x,y) (0,0) 1 - cos(x) + y4 (a)

A: Sol: Part (a) limx, y→0, 0x2+y51-cosx+y4Find two different paths to approach the point that gives…

Q: 1. Find the limit of the following functions: lim 00x/3+ cos x 1-cosx lim X-0 sin2x

A: To find the limit of the given functions

Q: Compute the following limits sin5x (1) lim- x→0 sin10x

A: We have to find Limit of given rational function using L'Hospital Rule of (0/0 form).

Q: B) Evaluate two of the following limits (Without using calcu 1 1) lim 1-cos2 x

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Q: I. Evaluate the following limits. x sinh x 1. lim x-40 cos 3x – 1

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Q: 2) Use the definition of the definite integral to write 2 e* dx as a limit. Do not evaluate this…

A: In this we use the limit  definition of definite integral

Q: 1. Use L'Hospital rule to eváluate the following limit: tan(t) In(cos(t)) dt lim tan(t') In(e“) dt

A: Use L' Hospital rule to evaluate the given limit.

Q: lim b-> -0.1x e 1.

A: Let I=limb→∞∫1be-0.1xdx

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

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Q: Find the limit, if it exists: 1 lim (7,y) → (0,0,0) 6 tan x² + y² + z² (Give the answer in exact…

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Q: Express the limit as a definite integral. n 7 lim 8 1 + i = 1 n- o n dx

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Q: What is the limit of (e^x-e^-x)/( sin (x)) as x approaches 0?

A: we have find the value of limx→0ex-e-xsin x

Q: Find the value of the following limits: 5y 1-limy→o tan 10y 2-limx-0 6x cot3x 7x²+8x 3-limx-0 4x²…

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Q: Express the limit as a definite integral. 7 lim n- 0 n 3 1 + (i/n) i = 1 '1 7n dx 8.

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Q: lim; 0 (, cos t, In t). t+1

A: limt→01t+1, cost, lnt

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

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Q: 4. Evaluate the limit of as e approaches 0. 2a A 2 B. % CO D. infinity

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Q: Evaluate the limit (1 – cos x)² sin² . lim x2(1 – e)4 COS X - -

A: Given limit is : limx→01-cosx2sin2xx21-ex4  To find the value of the limit.

Q: Find the limit. (To enter -∞ or o , type -INFINITY or INFINITY. Enter DNE if the limit does not…

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Q: Evaluate the following limits. sin- (e") 1. lim 2 V1- e20 1 1 x + sin 2. lim

A: On solving this we will get

Q: Find the limit. sinx cos 4x lim x-0 x + x cos 5x A) 3 B) 0 C) D) Does not exist 4/5 -/2

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Q: (c) Find the following limit: Vx +1- 2 lim X-3 x(x - 3) V9x2 + 5 lim x-00 X- 1 cot 0 csc lim sin e

A: Given we have to find the limit

Q: Find the limits

A: Limit: limθ→∞cos θ-1θ

Q: e* + e * — х2 — 2 lim —х sin?x – x2

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Q: 1. Find the limit of the following functions: lim x + cos²x 1- cosx lim e sin2r

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Q: cosx * sin? (3x) 2 2. lim x→0 x2

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Q: 5. Evaluate the following limits: sin(6x) а. lim x→0 5x3-4x cos e – 1 b. lim sin 0

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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: What is the limit as t goes to 0 of    4 tan^-1(t)

A: Topic:- limit

Q: 2. The limit of the following function equals: x2/3 + x-1 lim x--00 x2/3 + cos2 x

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Q: 4) If y = (x² + 1)cos(3x), then find dy/dx. 5) Evaluate the following limit e cosx – 1 lim x-n/2 2x…

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Q: | sin(ln 0) d0

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Q: Find the limit. e-4t i + lim t→0 j+ tan(5t) k sin?(t)

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Q: Find the following limit limx→0 (1/sin x − 1/x)

A: limx→01sinx-1x=limx→0x-sinxx·sinx=0-sin00×sin0=00

Q: 1. Compute the following limits (without using L'Hopital rule): sin(ræ) Va +4 – 2 (a) lim (b) lim 0

A: Use limit to solve

Q: 11) lim sin²y Y→TT 1+cosy

A: sin2y=1-cos2ya2-b2=(a+b)(a-b)

Q: Determine the limit. 5Tt 9) x→-T/2 lim COS cos (tan x)

A: Given  The limit is

Q: Find the limit. TTX lim cos 6.

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Q: q//// find the limit of the following: 1- lim x* cos 2 n→0 2- lim Vx2 + x3 sin-

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Q: By using The definilion of the D Lim x (X+1)= o 2) Lin x Cos

A: Given: 1)limx→0x(x2+1)=02)limx→0x cos1x=0

Q: 4. Evaluate the limit: lim sin arctan x V2 b. 2 1 d. DNE a. C.

A: Evaluate the given limit.

Q: I. Evaluate the following limits. x sinh x 1. lim x-0 cos 3x -1

A: Since you have asked multiple questions, as per Bartleby guideline, we are allowed to answer only…

Q: Given. lim e = 2e Use only E- & depini tion of a function limit to Prove: e*+1 dx d e?*** 2a+1 ニ2e…

A: epsilon delta ε-δ - definition of limit Let f(x) be a function defined on an open interval around a…

Q: Find the limit 1- sin z In (100r² + e*) (a) lim (b) lim 1+ cos 2r 100z

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Q: Calculate the limiting value for 1 cos(x*) – 1+5x³ lim x→0 х16

A: