5) Find the indicated limit if it exists. Vx+4 – 2 a) lim x→0 8x' + 27 b) lim x→-1.5 2x+ 3

Q: Find the limit of sin(6x) limy→0° sin(2x)

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Q: By considering different paths of approach, show that the limit xY COS Y lim does not exist.…

A:

Q: 4) Find the value of a for which the limit lim x→0 evaluate the limit. sin(ax)-sinx-x x3 is finite…

A: To Find: The value of a for which the limit limx→0sin(ax)-sin(x)-xx3 is finite and then evaluate the…

Q: 2. x- 4 lim tan(rx)

A:

Q: Find the limit. sin (3y) lim 4y

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Q: 1) Show that the limit doesn't exists : ysinx 3) lim (x,y)→(0,0) x²+y2

A: To show that the limit of a multivariable function does not exist,…

Q: 4) Use L'Hosp9tal's Rule to find the limits c) lim tanx)) メ→0 d) lim (ex + メ メ→ o

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Q: 2. Find the limits. limx→-1 sin(x² + 3x + 2) x³ + 1 M

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Q: Find the limit. -5x cos(x) lim

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Q: B) Find the limits by using L.Hopital rule : 7x 1. lim x→0 sin 2x

A: Here we will find out the required value.

Q: Find the limit. Enter DNE if the limit does not exist. 15zy lim (2,9) → (0,0) 22+ y?

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Q: Estimate the limit numerically or state that the limit doesn't exist lim h→0 cos(9/h)

A: We will pick some values for x. Then we will find values of y for those xs.

Q: Find the limit. lim zey cos 2x cos 2x P-(T.0,2)

A: limx, y, z→π, 0, 2ze3ycos2xPlug in the value x, y, z=π, 0, 2=2e3· 0cos2π=2

Q: Find the limits by using L.Hopital rule : 7x 1. lim x-0 sin 2x x2-16 2. lim x4 (Vx+5)-3

A: We need to find the limits of the given expressions by using the L.Hopital rule. For (1),

Q: 1 Q.3: Discuss the limit of f (x) : at x = 0", 0*,-∞,+∞, with graphs.

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Q: 2. Find the the limit. li -y 1 (tany): 2 Y- 2

A: Given that:                limy→π2-(tan y)π2-y

Q: 2. Find the limit or show that it does not exist: lim (2,y)→(0,0) 2x6 + y?

A: We have to find limit

Q: B) Find the limits by using L.Hopital rule : x²–16 2. lim x→4 (Vx+5)-3

A: The function is a rule that associates or fixes a number to the particular point x. If , then the…

Q: Q3 :(A): By using " L' Hopital rules "; Find the limits of : 1 (1) limx-o[: 1-cos x 2 sin²x

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Q: Express the limit as a definite integral. lim xk Ax [-3, 2] 4-0 k 1

A: Given

Q: b) Use L'Hopital's rule to find the limit: 1/In x (In xv lim

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Q: Find the limit.

A: Given- x→lim0 sin3xx To find- the value of the above limit. Formula used- Using the standard form as…

Q: 6. Calculate limit: lim tg x X→0 2-V4+3x

A: Here we have to calculate Limit =limx→0 tgx2-4+3x

Q: B) Find the limits by using L.Hopital rule: 7x 1. lim x-0 sin 2x x2-16 2. lim x-4 (Vx+5)-3

A:

Q: Evoluate the limit of (1-cosx) (x²) as x pproaches 0.

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Q: 1) Show that the limit doesn't exists : 3x2 y lim (x,y)-(0,0) x2 + y2

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Q: Calculate the limit and show proof. lim (1,1)(0,0) r2 + y?

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Q: Q2: (a) By using " L' Hopital rules "; Find the limits of ::- (1) lim-(7/2)-(tan x)cosx (2) limy-0…

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Q: 3x²+2x- 3 3. prove that with the help of the limit definition (with necessary analy si)

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Q: By considering different paths of approach, show that the limit lim (1,y)→(0,0) rª + y² does not…

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Q: B) Find the limits by using L.Hopital rule: 7x 1. lim X0 sin 2x x2-16 2. lim X+4 (VI+5)-3

A: *to find :- limits, using L-Hopital rule.

Q: By considering different paths, show that the limit doesn’t exist. lim (x,y)→(0,0) xy cos y/ 3x2+y2

A: Answer

Q: B) Find the limits by using L.Hopital rule: 7x 1. lim- X0 sin 2x -16 2. lim X-4 (Vx+5)-3

A:

Q: 4x2 [cos (2)* 1. lim X→+00 Find the limit using L'Hopital's Rule

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Q: Estimate the limit numerically. x² lim x+4 O diverges to +o 00 O diverges to -∞

A: Given

Q: Find the limit by rewriting the fraction first. x- y + 5/x - 5Vy lim Vx - Vy (ху) -- (0,0) x#y x- y…

A: limx,y→0,0x-y+5x-5yx-y =limx,y→0,0x-yx+y+5x-5yx-y =limx,y→0,0x-yx+y+5x-yx-y

Q: lim 0-4 In[(1 + h)² + 1] - ln(2) y

A: To evaluate the given limit .

Q: 1) Show that the limit doesn't exists : 3x2 Jy 2). lim (x,y)→(0,0) x2 +y²

A: We have considered different paths y = mx. If the limit is independent of m then the limit shall…

Q: Estimate the limit numerically or state that sec (x) lim x→1+ vx³–1 (Enter DNE if the limit doesn't…

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Q: Estimate the limit numerically or state that the limit does not exist (DNE): sin(12r) lim

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Q: 1e. Use L'Hopital's Rule to find the Limit: lim (1+4x)3/pi x->0

A:

Q: 1c. Use L'Hopital's Rule to find the Limit: lim          (1 - x)tan(pix/2) x->1-

A: We will use tan z = 1/cot z formula

Q: Estimate the value of the limit lim, 40 COS x if it exists, by filling out this table and then…

A: We have to find the limit of the function and want to find some values to conclude graphically.

Q: - Find the limits using L-Hopital's Rule: cos 3x 1 (а). im $ x→0 X* (b). lim (e - 1)*

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Q: 4. Use the € & definition of limit to show that lim (2z+3i) = 2 + 5i. z+1+i

A: As per our guideline, we are supposed to solve only first question. Kindly repost other questions as…

Q: 1f. Use L'Hopital's Rule to find the Limit: lim (tanx)x x->0+

A: Given,

Q: B) Find the limits by using L.Hopital rule : 7x 1. lim 0 sin 2 -16 2. lim 4 (V+5)-3

A: 1. Here limx→07xsin 2x is of 00 form, so by applying L. hospital rule, we get limx→07xsin 2x =…

Q: Determine the limit: lim 4x2 x→0 sin (2x) cos(2x)

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Q: Q1:Find the limit using L Hopital rule In (csc x) lim xT/2 (x – (1/2))²

A: Given limx→π2ln(cscx)(x-π/2)2 We have to find limit by using L Hospital rule L'Hospital's Rule…