Q 4. (a). Show that limit *1, does not exist if (5-4x S(x)=. -)- {ax-2 for x <1] for xz1]

Q: There is a jump discontinuity at x = 1 and lim f(x) = 1

A: At X=1, there is a jump discontinuity.   limx→1- f(x) = 1.As function f(x) approaches towards 1 from…

Q: 3 Find the limit: lim t 3 et – 1 - (Enter undefined if the limit does not exist.)

A:

Q: Formally prove that lim 2x+3=7 using the ɛ,8 definition of a limit. x→2

A:

Q: 5. Consider the limit: lim x² = 16. What is the largest allowable & that will "work" for e = 0.25 in…

A: Given  f(x) = x² To find : Value of delta using definition of limit

Q: Show that the following limit fails to exist by showing that the limit is different for two…

A:

Q: Pick 8 of 10: Prove or provide a counterexample. lim Sn =0 if and only if lim s,=0

A:

Q: how did you get y^2-4xy to y-4x when there are three y's on top I input the numbers and got 0 which…

A:

Q: Express the function n, lim n→+∞ 4k² in closed for and then find the limit. n³

A: We will first write this function in closed form then we will calculate the limit of the function.

Q: The limit as x approaches infinty of (x+3^x)/(x^2-3^x) Evaulate using L'Hospital's Rule providing a…

A:

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

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Q: 3. Determine the infinite limit. x² + 3x lim x--1- x2 + 2x + 1

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Q: Evaluate the limit /9nt + 13п3 — 5n - 10 lim n-10 -V25n16 + 5n² – 9n Also, find the asymptotic value…

A:

Q: limit as x---3 for the function (x-2)^11/(3-x) using L'Hopitals.

A: Consider the given function (x-2)11 / (3-x).

Q: limit as h---0 for the funtion ((e^2h)-1)/h using L'Hopitals

A: We need to evaluate the given limit using L'hopitals rule. As per L'hopitals rule, if we get 0/0 or…

Q: Compute limit as x goes to infinity of (cos(x))/(x)

A: We find: limx→∞cosxx We solve this limit by using Squeeze theorem. Squeeze theorem states that if…

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

A:

Q: find the indicated limit using l hopital rule

A: Given

Q: Evaluate the limit 9n4 + 13n3 - 5n – 10 lim -V25n16 + 5n² – 9n Also, find the asymptotic value of…

A:

Q: 4. Show that the following limit does not exist by using two paths y = 0 and x =-y lines. x2 lim…

A: We use path y = mx.

Q: Draw the graph of a function f on [0, 4] with the given property. Infinite one-sided limits at x = 2…

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Q: What is the limit as x goes to infinity of (ln(x3 + 9) - ln(2x3 + 17x))?

A: Use quotient rule of logarithm to reduce the function as shown,

Q: What must be multiplied to both numerator and denomination of lim→2 3-г-1 SO 2-x that the limit will…

A: We have to find multiplication factor for given Limit.

Q: Determine the infinite limit. limit as x approaches 3 from the right side of ln(x2-9)

A: We have ln(x2 - 9 ) if we take x as √10 which is approximately equal to 3.16, then, x2 - 9 =1…

Q: In(1+ x?) lim x-0 x3

A:

Q: compute limit as x goes to infinity of xe^-x

A: Given,            limx→∞x e-x

Q: 8. Use L'Hopital rule to determine whether the limit exists, and evaluate it if it does. 1 - t lim…

A: Given,          limt→0et-1-tt2

Q: Prove that lim 4x – 2 = 10 using the epsilon-delta definition of a limit.

A: Let, ε&gt;0 is any number. and δ&gt;0 is also a number. For the given limit, fx=4x-2a=3L=10 From ε-δ…

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

A:

Q: Give an example of a limit of the form 0/0 that convergesto 1 as x -&gt; 0.

A: Given: Rx=fxgx is a function such that limx→0Rx is of the form 00 and converges to zero. To…

Q: 2. Find the indicated limit using l'Hopital's Rule: In cos 3x 2x lim

A: Now , We  will find the limit using L.Hospital.Rule  .

Q: e4x – 1- 4x lim x2

A: topic - limit using l 'hospital rule

Q: 9 -x2 if x 1 .What value of c makes g(x) continuous at x = 1? Show all conclusions. 2 Vx-4 Using…

A: For a function to be continuos, the left hand limit should be equal to the right hand limit.…

Q: 5.3. Show that when a limit of a function f(z) exists at a point 2o, it is unique.

A:

Q: Vx+14-4 Compute the limit analytically without L'hopital's rule: lim X-2

A: Given limit is : limx→∞x+14-4x-2 To find the value of limit.

Q: 2. Find the limit of the following function by using L’Hopital's Rule. In x lim - х>0 CSC X

A:

Q: The limit fx= X2 XスT 2メ-ズ Cos X ,X < TI at Will be 1-itexisted and eanals T 2-It existed and equals…

A: In the question we have to find correct option.

Q: Q3 :(A): By using "L' Hopital rules "; Find the limits of : (2) limx-o x-³ (tan-¹x - x)

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Q: In(x/4) z+4 x2 – 16 (Enter undefined if the limit does not exist.) Find the limit: lim

A: Solving the problem by finding the limit of the given expression.

Q: Find the limit. lim x--> infinity  e3x+5/4e3x+ex-7

A:

Q: Estimate the limit numerically or state that the limit doesn't exist: 2²–5x-14 lim 1²-6x-7 (Enter…

A: find the limit of the function.

Q: Evaluate the limit 9n4 + 13n³ – 5n – 10 lim -V25n16 + 5n² - 9n Also, find the asymptotic value of…

A:

Q: x-3x+5 by X-0 4x2+2x+3 10. Find the limit: lim means of the L'Hopital Rule

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Q: (a) Find the limit (if exist): lim "(2t-2)2 dt 2x-1

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Q: yA - 2x? lim 4 - 2х 2 (х., у)- (0,0) у +х 4

A:

Q: Discuss the continuity of : Q1 x+ for *く0 for osr 2 Q2 1-x lim

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Q: Find the limit: limx→0​ x3sin(1/3x​3)

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Q: 7 Find a limit equal to V4x – 3dx. 3

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Q: -x e lim In(1+4e-x)

A: The answer is 1/4

Q: 5) Find the indicated limit if it exist. а) lim X-2 3- Vx+ 7 2 - x x' +1 b) lim x-- x+1

A:

Sequence and Series

A sequence is defined as a collection of things. Series is defined to sum the things one by one in the sequence.  It was invented by German mathematician Carl Friedrich Gauss.