(b) Prove that lim,→20,¤€A ƒ (x) exists and is equal to lim→0 Yk-

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

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Q: If || fn-fl|p. os no prove that lim 11 fn V = || f 11 p. له در

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Q: Theory and Examples

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

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Q: x – 4 8. Prove that lim Vx = 2 using the e-d-definition. Hint: Va – 2 = VT + 2

A: The epsilon-delta definition of limits says that the limit of f(x) at x=c is  value  of limit. if…

Q: find the limit of g(x) as x approaches the indicated value.

A: ltx→-25-x2gx=0As x tends to -2 denominator tends to 1 .    gx≠0 . gx>0

Q: 1. Use the definition to show that x² - y² lim (x,y)→(0,0) x² - y² = 0.

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Q: Use the Squeeze Theorem to find limx→c f(x).

A: Given that 4-x2≤f(x)≤4+x2 To find the limit of the function using the Squeeze theorem when x→c=0.

Q: In (x +h) – In (x) is When x = 2e, lim h→0 h

A: Substitute x=  2e above

Q: Find the limits in Exercises 1- 3x2 – y² + 5 (x, y)→(0,0) x² + y² + 2 2. (x, y)→(0,4) Vy 1. lim lim

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Q: lim,y→0 sin x

A: I am attaching image so that you understand each and every step.

Q: If f(x) is differentiable at X =c then lim f(x) must exist and f(c) must be defined

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

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Q: Assuming h > 0, compute Vx - Vh lim x→h X-h (a); Vh (b). 2h (c) (d) 2h (0)

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Q: Find the value of the limit: 3x -9x e -e lim In(1+x)

A: Using limit to find the value of given function

Q: find the limit of g(x) as x approaches the indicated value.

A: limx→13x2+1gx=∞

Q: (-1)"f" cost =1--+ 4! 2 (2n)! In(1+t) =t-+ 3 -.+(-1)*-"4 +... n Yukarıda verilen cost ve In(1+x)'in…

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Q: Please

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

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Q: パーy (x.y)-(0,0) x + y 2.) Prove that lim does not exist.

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Q: draw the graph of a function on [0, 5] with the given properties.

A: Removable discontinuity at any point (a) of domain of function (say f(x)) is define as Graphically…

Q: 2) If x3 s f(x) sx for x in [-1,1), find lim f(x) if it exists. x-0 A) 0 B) Does not exist C) -1 D)…

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Q: Verify numerically that:

A: To verify: limh→0eh-1h=1

Q: Use the Squeeze Theorem to prove lim = 0. x00 x+ e- For x 0, since 0 < e* <1, we have

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Q: Exercise 6. Find the limits. 1 dx. 1+ x2n lim

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Q: 2. Calculate the limit algebraically. x-11 lim O -1.8 03 -0.6 O 1.8

A: Given

Q: Find the limit of lim((9+3x)1/2-3)/x as x approaches 0

A: To determine the value of the limit.

Q: 2. Use Squeeze Theorem to find lim,x f(z), if for all z >4 6e - 15 < {(x) < VI- 2 2e

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Q: Prove, using the formal definition, that lim→-1 (T+1)² +0o. %3D

A: We have to find the limit limx→-13x+12=+∞.

Q: Find the maximum value of & > 0 that satisfies the limit claim corresponding to e = 0.3, that is,…

A: In the question it is asked to calculate the maximum value of δ for the given function limx→59-x5=8

Q: x-y (x,y) →(0.0) x + y 2.) Prove that lim does not exist.

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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: Find the value of the positive constant c such that....

A: Given- limx→∞x-cx+cx=14 To find- The value of c. Concept Used- If any limit of the function fxgx in…

Q: ow that lim (x,y) → (0,0) 4 3x² + y² 5y does not exist.

A: To show that limit does not exist.

Q: 1. Investigate the limiting behaviour of x2 lim (x,y)¬(0,0) x2 +3xy +y2

A: It given function fx,y=x2x2+3xy+y2. When x,y=0,0 in fx,y=x2x2+3xy+y2 will result in 00. Set the…

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

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Q: Consider the function 2+2+17-2ry+v² if (r, y) # (0,0) f(r,y) = if (1, y) = (0,0). (b) Find…

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Q: 2. Use Squeeze Theorem to find lim, x f(z), if for all z > 4 Ge² – 15 < {r) f(x) < VE-2 2e

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Q: show that lim(x,y)→(0,0) (x^3+xy^3/x^4+y^2) does not exist.

A: We will see that along y=mx2 path limit does not exist which means limit does not exist.

Q: Suppose that functions g(t) and h(t) are defined for all values of t and g(0) = h(0) = 0. Can…

A: Given that functions g(t) and h(t) are defined for all values of t and g (0) = h (0) = 0.

Q: Use continuity to evaluate the limit. lim In(2 + V1 + x)

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Q: Find the maximum value of 8 > 0 that satisfies the limit claim corresponding to ɛ = 0.1, that is,…

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Q: Prove, using the formal definition, that lim,→1- V1– x = 0.

A: Given, limx→1-1-x=0

Q: Зу Let flx,y) = , find the lim(xy)¬(-1,1)( Зу %3D x+y' ) along the curve y=x² .

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Q: . For a function f, suppose lim f(x) does not exist because values of f(x) oscillate between two…

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Q: Consider g(x)=−7x3+7x2+9. a) limx→0−g(x)= b)limx→−1−g(x)= c)On what interval(s) is g(x)…

A: It can be solved using the limiting definition of continuity

Q: Find the limit. lim (e 4/x+ 9x) x/2 x-0 0 1 00 e2

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Q: Prove that lim n 00 a" f (x) dx = 0, for any f E R[0, 1].

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Q: lim(x,y)->(0,0)  (4x2y)/(x2+y2)1/2

A: Given: lim(x,y)→(0,0)4x2yx2+y2         (1) To compute: The limit.

Q: Find the limit x-1 lim x>I* Vx +2

A: