can this be evalnated by using L'HOSpital's Ruie? lim Trxln(x) Itxen(x) (メ-)nx

Q: 1-z = ? What is lim %3D !- 2!- -2

A: In order to evaluate the limit of a function f(x) at certain point a then replace x by a to get…

Q: What is lim x=inf (x_n) and y=lim sup (x_n) where x_n = [(-1)^(3n)] + 2? (express answer as x,y)

A: Solve the following

Q: Show that lim (x,y) →(0,0) 16x4 +9y¹2 4x² + 3y6 does not exist.

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Q: 2) Show that the_lim. 1) xy2 lim (x,y)→(0,0) x² +y²

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Q: What is lim1 f (x) ? X

A: Find your answer below

Q: Find limx->∞,if for all x>5

A: We apply limx->∞ on all sides.

Q: Use l’Hospital’s rule where applicable to find the limit.

A: the given limit is: limx→08x6+3x4-9x9x7-2x4+x3 we have to evaluate the given limit.

Q: Prove that lim, = 1, (x > 0).

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Q: use L'HOSpital's rule ro show that lim 2tanx イ→ % rc 2x

A: We have to proof

Q: Show that lim (x,y)→(0,0) 16x4+9y12 4x²+3y6 does not exist.

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Q: What is lim x-inf (x_n) and y=lim sup (x_n) where x_n = [(-1)^{3n}] + 2?

A: We have to find the lim inf and lim sup of sequence

Q: Find limx→−∞(x2 −1)e4x. Show work.

A: We need to find : limx→-∞(x2-1)e4x

Q: Find the lim inf (xn) and lim sup (xn) of Xn=3-(-1)"

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Q: Find lim (√2-t, et-¹, In(t + 1)) t-0

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Q: what is lim of x approaches -8 from the left of 7x+56/abolute value of x+8

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Q: V2x -1 Using defination of limits, prove that lim Jx- 3 L^ = x4

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Q: lim (In w-

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Q: Prove limx→∞(1/x)=0

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Q: Is there a value of a for which limx1 3x^2+ax+a+3/x^2+x-2 exists? Enter the value of a if such a…

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Q: If f(x)=x2−9x−3 , what is limx→3+x2−9x−3 , limx→3−x2−9x−3, and f(3) ?   Is f(x) continuous at 3?

A: Given,              f(x) = x2 − 9x − 3

Q: メ-D4 xー12 In do torminate Form Lim | १ - 3

A: Given:   Limit equation is given

Q: swer of the following lim 2x²+6y² lim (x,y)→(0,0) x²+y²

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Q: V2x –1 Using defination of limits, prove that lim Vx- 3 L^ = X4

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Q: Find the Limit: 1. lim (2x + 5) x--7 3. lim(-x + 5x 2) 5. lim 8(t - 5)(t - 7)

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Q: Find lim *2 x -2 In(x- 1) by using the La'Hospital Rule.

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Q: Show that 16x4+9y12 lim (x,y)→(0,0) 4x²+3y6 does not exist.

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Q: Fird the domain of f (x) = 2-Vx2-5 Solve lim x→-3 =? (Don't use L'hopital Rule) x+3

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Q: b) sin (2x) tan (5x) Find lim- (Can't use L'Hospital's Rule)

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Q: . Is it possible that f(2) = 5 but limx→2 f(x) = 7? If so, what kind of function can satisfy this?

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Q: Show that 2 x² - y² - 1 lim (x,y) →(1,0) 1 − x + (2y)² - does not exist.

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Q: Hws] lim x = 5 E 5e •Prove

A: Given sequence xj=5j-1j+2j∈N we have to find limj→∞xj limj→∞5j-1j+2=limj→∞j5-1jj1+2j       (Taking j…

Q: lim cas z is nonexistent

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Q: Find the limit. x2 - 8x + 15 x3 - 9x lim - 00 O 15 Does not exist 8

A: First factor the denominator and use limit of two sided limit approach,

Q: Evaluate the limit: lim 3z4 – 8z = - %3D Z - 1

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Q: Show that lim- e +1 does not exist. 1/x

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Q: Find the limit or show that it doesn't exist. 1-х-х2 a) limx→-o 2х2-7 V1+4x6 b) limx 2-х3

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Q: The infinity in the V6-ydy can be eliminated by applying lim V6-y dy O True False

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Q: —ах+6 if x2-1 Let f(x)=< For what value of a does 2x2 +ах ifx<-1 lim f(x) exist? x--1

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Q: Suppose that lim as x approaches infinity of f(x) + x^2 = L for some number L. Then lim as x…

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Q: Use basic techniques to find the limits. 8. lim(-7) X-3 9. lim (x³ + 2x) X→-1 10. lim cos x

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Q: Find the limits limx→0+x tan (π/2 - x)

A: Given that, f(x)=x tan (π/2 - x) We have to find, limx→0+xtanπ2-x

Q: Use continuity to evaluate the limit. 8 + Vx lim 8 + x

A: We have to evaluate limx→18+x8+x Important formula  If fx is continuous function then limx→afx=fa

Q: Find the limit or show that it does not exist. lim √25t² + 2 − 5t t-x

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Q: We have lim I- a Vsing 1-x = (- Fa)(+Ta) So, lim 1- Fa lim - a 거- (1-「 (i+Tx) %3D lim ス→) as 1+ T…

A: Yes your solution is correct

Q: 2) If 2 – x2 < f (x) < 2+ 3x² whenever -1 < x < 1, use limit theorems to find lim0 f (x). Give all…

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Q: lim (Vx2 + 4x + x)

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Q: 3-Vx2+9 Without using L'Hopital's rule, find: lim-

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Q: Use the definition to show that x² - y² lim (x,y) →(0,0) x² - y² 0.

A:

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.