QUESTION 6 1-Z What is lim = ? i+1 i- 1 2i i-1 1-i

Q: 5x - 1 Let f (x) = %3D X +3 Find f' (x). First set up the limits and simplify the first one. Using…

A: The function given is: fx=5x-1x+3 a)-…

Q: Question 9 sin(ax) Evaluate lim where a< x-0 Xsin(x²)

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Q: Question 3. Construct examples such that lim(p, + qn) limr, + limyn

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Q: ) lim- 1 5 arctan -4arctan |=? Use L'Hospital's Rule 4 X-0 xVx

A: L'Hospital's Rule tells us that for calculating limit of a function if we have an indeterminate form…

Q: b) lim

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Q: Question 1 a. Evaluate. i. ii. i lim X0 (-81+(x-9)21 (16-x2) lim X→-4 16+4x/ lim x→0 3-Vx²+9 2

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Q: Question 3 Let x – 1 2? – 4x + 6 if x > 2. if x < 3 f(x) = { Determine 3.1 lim,+2- f (x). 3.2 lim,2+…

A: The given function is -  f(x) = x-1if x&lt;3x2-4x+6if x⩾2We have to find the following - (a)…

Q: Question One: (i) If lim- 3x sin (ax) = 5 = lim- tan (2x) find the values of a and b. x-0 x-0 bx-x

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Q: Question 2 [2,3] Clearly show how you use the limit laws and write down all your steps. (1) Evaluate…

A: Given: To Find: To evaluate the given limits.

Q: QUESTION 6 | 16-ydy can be eliminated by applying lim t+ -0 6-ydy The infinity in the O True O False

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Q: 1-cos 3t 1. Evaluate lim by constructing table of values. 3t t -1 -0.5 -0.01 -0.001 f(t) 1 0.5 0.01…

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Q: Question 4 2 i (z-i) lim z?+1 1 O 2i

A: 1 Just use L'Hospitals rule.

Q: Question 1. Evaluate 3-Vx+5 (a) lim X4 x-4 tan 7x (b) lim X0 7

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Q: Question 28 1-x2 Evaluate lim x²– 2x-1 A 1 B None of the given choic

A: We have to choose the correct answer from the given option according to the given condition

Q: tan 5x Evaluate: lim A. -5 X-0 sinx В. -1 С. 1 D. 5

A: There two results of the limit  If  limx→0tan xx , then  limx→0tan xx = 0  If  limx→0sin xx , then…

Q: 2 i (z-i) lim z?+1 1 -1 о 2i

A: 1 Just use L'Hospitals rule.

Q: Question 16 Suppose that b is a constant such that x3 + bx + 2 lim -1 (x – 1)2 l, %3D where l is…

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Q: Question 9 Evaluate: lim 0 2x 222. None of the choices 1 2 0 -1 +x

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Q: Question 7 of 10 Evaluate lim 2-2 0 x-2 5x-2-√√/2x+4 / Ə

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Q: Question 4.[4, 4 marks] Evaluate the following limits, 1+ x (a) lim [r – a* In(-")I (b) lim(1- 2r)

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Q: 0, 5. Let f(x) = sin, x> 0. . y = Jain . a. Does lim, 0 f(x) exist? If so, what is it? If not, why…

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Q: a) lim

A: We know that 1/∞ =0

Q: sin no 73. Investigate lim numerically for several positive integer values of n. Then guess the…

A: Given: The limit is limθ→0sinnθθ.   For n = 1. limθ→0sinθθ=sin00=00   Apply L'Hospital rule.…

Q: Question 4 x3-8 :- If fx)=x-2 If x1. x+1-

A: Given :

Q: S 1. lim 2 I- I - 2 1.9 1.99 1.990 2,001201 | 21. 12 2, lim 19 1.99 1.999 201 1211

A: Please see the explanation below

Q: Question 1 1 lim z5 X-5 0-

A: To find the limit (x tends to 5) 1/(x-5)

Q: 1-z What is lim = ? !-2!-2 i-1 2i i+1 i-1 O 2 1-i

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Q: Prove the ratio test (Theorem 7.2.3a). What does this tell you if limn-co |#n+1/xn| exists?

A: As per the question we have to prove the ratio test which is used to determine if an infinite series…

Q: 1-z What is lim = ? !-2!- +2 1-i i-1 2 i+1 i-1 2i 2. 2.

A: Option (b) is correct

Q: A = lim %3D i = 1

A: Given that: The equation is f(x) = x 2 e x  ,     0 ≤x≤3 .

Q: Question 5 What is the limx→ [(ln(2x - 4)) - (ln(x+3))]? If your answer is a Whole Number Fraction…

A: limx-infinity [ln(2x-4)-ln(x+3)].

Q: Question 11 Evaluate the limit: lim h→0 Question Help: Video (-5+h)² - 25 h

A: We can solve this as follows:

Q: 1) Calculate: lim E-1(5+ 3i) (÷) showing all work. i=1

A: Since you have posted multiple questions, as per our policy we will answer first question. Please…

Q: evaluate the limit.

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Q: Question 30 1- cosx Evaluate lim

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Q: Question 14 2- 4x +6 x2 1-2 A) 2 B does not exis C) None of the given choices D 1 E E -2

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Q: 0, 5. Let f(x) = sin, x > 0. х fo. Tsin4. 0, y = sin =, x>0 a. Does lim,,0* f(x) exist? If so, what…

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Q: QUESTION 6 Choose the most correct answer from below lim x+1 X-1 Does not exist None of these.…

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Q: Question 8 Evaluate: lim-1 (3-22)tan (7). e 3m 01 O None of the choices O e

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Q: Question 5 The values of k and m such limx-e k-m In x %3D e-X °k=-e, m = e m3D k = -e, m = -e ok=…

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Q: 9 sin 4x lim ] (Type an exact answer.) 5x

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Q: a + cos bx Find all values of a and b such that lim -1. x2

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Q: Question 4 2 -Vx+1 The value of lim is the same as x- 3 x+ 3 1 - lim x+ 3 Vx+1 + 4 A B None of the…

A: The given expression is limx→32-x+1x-3.

Q: Question 8 Saved If limx→a f(x) 8(x) = 1 and limr-→a g(x) = 0 then, we must have limx→a = True False

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Q: I - 4 Prove that lim vI = 2 using the e-d-definition. Hint: Va - 2 = VT +2

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Q: 1 (iii) lim I-bt 6 – x

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Q: Recitation Week 4 Discussion Problems - 40. Prove that lim esin(r/r)=0.

A: squeeze theorem:

Q: Question 18 How do we transform lim (x-- x*) in evaluating it. This yields an answer of. (A by…

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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.