J6 - V5h? +11h +6 lim- x→0 h

Q: Identify the removable discontinuity. x2 – 16 f(x) : X – 4 (x, y) =

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Q: xY lim x,y)→(0,0) Vx2 + y? 2

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Q: 3tan z sec? x dr 2.

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Q: x V1+t?dt lim x+2 =? х2—4

A: Given the term : limx→2 x ∫x21+t2dtx2-4 We need to evaluate it.

Q: (c) lim (x.4)→(0,0) xª + y6 – x²y² °

A: The limit to evaluate is: lim(x,y)→(0,0)x4y2x4+y6-x2y2 Path-1:…

Q: y2 – 9 lim V 2y2 + 7y + 3

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Q: Find Souution of ODE xy"+y't x²y 20

A: Given, the differential equation                  xy''+y'+x2y=0                 ...(1)

Q: 7y lim 2 y>+∞ +3y+Vy-4y

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Q: x² + 1 dz x +1 ,2

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Q: (b) lim (z.y)→(0,0) Vr4 + y3 +1–1

A: limit of the rational function

Q: z + 14z + 49 f(z) = f(7) =| lim f(z) = 1. %3D z2 - 14z + 49

A: Since you have asked multiple question, we will solve the first question for you. If youwant any…

Q: y = 2sinx and y = 0 from x = T to x = 4 π 2

A: The given curves are y=2sinx and y=0 from x=-π4 to x=π2. So, the bounded region is as shown below;…

Q: Q4 / Vx+1–1 A ) Find limx→0

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Q: /2x – y – 2 (b) lim (2r – y + 4) (1,y)-(2,2) 2x – y – 4

A: We can directly put the value of (x,y) if denominator is not becoming 0. Or else, we can choose a…

Q: 2t dt = 1 – t4 lim x→1- A) B) 2 C) 0. D) 1. 1

A: Given limx→1-∫0x2t1-t4 dt

Q: Q3// Evaluate (a) lim,4 VE-2 S-V49 sin 3y cot 5y (b) limy-o y cot 4y

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Q: 2ry + 6x lim (z,v)(0,–3) r² + y² + 6y +9°

A: We have to use polar coordinates here.

Q: (t + At)2 – 7(t + At) + 3 – (t2 – 7t + 3) lim At0 At

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Q: d) lim f(x), where x-2+ (x² + x + 1 if x 2

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Q: f'lx) = lim - 2x + 2x %3D (X+Xxj? 2

A: To solve lim∆x→0-2x+2∆x(x+∆x)2, plug in the limit and obtain -2x+2(0)(x+0)2.…

Q: h(x) = Vx – 2 on the domain [2, 5]. -

A: The given graph is:

Q: Q2: Evaluate: 1 2 In cosy, [1] limy-o 7 + y4 'y2

A: Given, limy→01y2+2lncosyy4 now solve this limit limy→0y2+2lncosyy4 apply L-hospital rule…

Q: t t→0 et (c) lim = 1 True False

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Q: y — у — 2 3. lim f(y), where f (y) = y→2 y2+ у — 6

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Q: lim ( Vy? – y) y² + y +1 – y00

A: limy→∞y2+y+1-y2-y

Q: 5x - 5y2 lim (z.y) (0,0) 7z+7y () Limit DNE 0. O 5/7 O 5/7

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Q: y +7y2 +16y+ 12 lim y-2 y3 +5y? + 8y +4

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Q: (b) lim y - 2 y→2 5 – V27 - y

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Q: OLetL)%3DXD 3X-/0 when x+2-Fénd a value ff(2)that wall !! X-2 make fis Continueus at X-2

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Q: I Sdve for dy using the four-step rule 2. y = x"- x 5X-3 ソ= 4- 3X

A: We have to solve the problem

Q: ? lim (z,y) (1,1) 2x – ry – y r2 – y2

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Q: h 4 (b) Lim h→0 V5h + 4 – 2 5 ||

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Q: lim, - „f(x) = 0, then fx)dx diverges Select one: O True False

A: The given statement is

Q: Evaluate [ T 1-x² x² + y² dydx.

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Q: Find dydx for…

A: the given equation of the curve is: y3+y2-5y-x2+4=0 we have to find the value of dydx

Q: 5 Use implicit derivation to find y. x² +y +z =e"-

A: Given,           x2+y2+z2=exyz

Q: o three steps atthe Secaut £(X) X-2 Using X-0 %3D

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Q: Find the limit. 1 t1 5 lim 4e 4 1t t 0 t t LC

A: First we take the limit inside and simplify

Q: 2x2 + 2y? lim (x,y)→(0;0) V² + y² – 1 + 1 .2 -

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Q: I Y=t5メPYove th y-2(21くるど

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Q: 2 lim y→7L_– 4y – 21 3y Зу — 17у — 28 -

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Q: Suppose that 3x² - y² = t² and y=tsin 0. Find dy ().-0 (27). and X

A: Given 3x2-y2=t2 and y=tsinθ

Q: Vx - Jy +1 lim (x ,y )→(4,3) x -y -1

A: note : as per our guidelines we are supposed to answer only one question. Kindly repost other…

Q: . lim 4y9 + V y--00 /y18 – 1

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Q: x[ V1+t?dt =? 1) lim42 x+2 x2-4

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Q: Q9. Find y2 using Reduction of Order y" – 3.ry +4y = 0, Yı 1 = x?

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Q: y y =x – x12 1 Rogawski et al., Calculus: Early Transcendentals, 4e, © 2019 W. H. Freeman and…

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Q: Forf (x) = 2x +2, compute lim ƒ(1+h) –f (1) %3D f(I+h) -f (1) lim h>0 %D h

A: Given : fx = 2x+2

Q: 31-x 2. Evaluate [(x+ y)dydx . 1 0

A: To solve this question first we integrate w.rt dy then put limits and after this integrate with dx…

Limits

When it comes to calculus, limits are considered to be a very important topic of discussion. The main importance of limit lies in expressing the value of a function as it gets closer to a certain value. Also, limits can help you to understand other topics, such as continuity and differentiability better. In a broader sense, every calculus notion is a limit. Other branches of calculus have also been derived from limits.