71. GU In some cases, numerical investigations can be misleading. Plot f(x) = cos . (a) Does lim f(x) exist? x+0 11, 1 (b) Show, by evaluating f(x) at x = ±;,±;,±; that you might be able to trick your friends into believing that the limit exists and is equal to L = 1. (c) Which sequence of evaluations might trick them into believing that the limit is L = -1?

Q: 1-cos(0) lim 02 e-0 1 lim (1 + x)a x-0 If f (x) is continuous at a, then what is the value of lim…

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Q: 8) Evaluate the limits: a. lim x sin X00 ex-x-1 b. lim x3

A: As per the company policy i can answer only first question for you,more than that leads me towards…

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Q: 2-Given that: lim,-o ƒ (x) = 2 lim,--o g(x) = –-1.2 lim,-o k(x) = 0.8 Find: A- lim,-o[f(x) + g(x) –…

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

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Q: 5. Let {(2) = { * * x + 0 x + 2 x = 0 and o(e) = { * *' x + 0 x = 0. x +1 g(x) i. Show that lim,→0 =…

A: find the limits as follows  limx→0fxgx=limx→0x+2x+1=21=2 limx→0fxgx=2 now limx→0f'xg'x=limx→011=1…

Q: Find the one-sided limit

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Q: 43. Assuming that lim 4 = 1, which of the following statements is necessarily true? Why? (a) f(0) =…

A: Consider a f0=0Here if x=0 , f0=0Substituting in limx→0fxx=00Inderterminant formDifferentiate…

Q: 6. Find the limit of f(x) = -- 10 as x approaches co and as x approaches - c lim f(x) = X00 (Type a…

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Q: Find the limit, if it exists. (x² – 16 if x>0 Let f(x) =x2 -16 if x<0 x- 4 Find lim f(x). x-0- 00 -4…

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Q: (b) If we keep the first part of the hypothesis of Theorem 5.3.6(L’Hospital’s Rule) the same but we…

A: We have given that;

Q: 1. Let f(x) = 5, if x>1 f(x) = 2, if x < 1 f(x) = undefined for x = 1 Find the following one sided…

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Q: Consider lim e-. a) lim 4x - x² = 0 b) If we let t = 4x - , then we can rewrite the limit as lim of

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Q: 4. Find the limit, if it exists or show the limit does not exist: a) lim (x,y) (0,0) x + y* .2…

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Q: 7. Find the limit, if it exists. If the limit does not exist, explain why. sin (2x - 6) sin(4x12)…

A: To find if the limit exists or not. limx→3sin2x-6sin4x-12x2-6x+9 limx→5fx when limx→5fxx-5=3

Q: Show that the function f(x) = |x - 2| is not differentiable at 2. We have if x 2 2 f(x) = |x - 21 =…

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Q: 7. Find the limit, if it exists. If the limit does not exist, explain why. - (a) lim sin (2x 6)…

A: solution is given below

Q: 1. Determine the infinite (oo or -o) limit as follows: x² - 2 (a) lim x2-x² - 3x + 2 sin x 1 x+ cos…

A: Topic = Limits

Q: 4 (a) Evaluate lim,1 (금-) (b) Let f(z) = -r. Find the value(s) of z if the second derivative f"(x)…

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Q: Broadly speaking, what are the Limit Laws, and why do they help us calculate limits? 2. In Example…

A: 1.) Limit laws are very helpful in calculus i will explain you how.Suppose you know the limit of one…

Q: L’Hôpital’s Rule to evaluate the limit, or state that L’Hôpital’s Rule does not apply.

A: Given limit:

Q: 5. Find the limit, if it exists. If the limit does not exist, explain why. sin x - cos x (a) lim…

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Q: Can you explain how to do this problem? 1.8 35) Use continuity to evaluate the limit: lim x-&gt;2…

A: x*sqrt(20-x^2) is continuous at x=2 because x is continuous at x=2 and (20-x^2)= (20-2^2)=20-4=16.…

Q: Suppose g(x) is a function such that 2 cos x 0 (meaning: when x is close to 0). Use Squeeze Theorem…

A: Given,            Suppose g(x) is a function such that  2 cos(x) ≤g(x)≤2 + x2.

Q: How close to 0 we need to take x so that lnx0 but f(0) does not exist

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Q: he limit (if it exists). (If an answer does not exist, enter DNE. Round your answer to four decimal…

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Q: V-5 – x + 5 if x 6 - Calculate the following limits. Enter "DNE" if the limit does not exist. lim…

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Q: The function f in the given figure satisfies lim f(x) = 5. For each value of e, find all values of Q…

A: Given : limx→5fx=5To find: a) The values of δ&gt;0, when ε=2 such that fx-5&lt;ε whenever…

Q: Evaluate the limit of f(x) numerically or state that the limit does not exist. sin(5x) f(x) %3D бх…

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Q: QUESTION 2 Prove using the definition of a limit that lim x² + y2 -y = 4. >

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Q: 7. Find the limit, if it exists. If the limit does not exist, explain why. (a) lim sin (2x6) sin(4x…

A: Explanation of the answer is as follows

Q: 1) Find the limit as x approaches 2 from the left and from the right (if they exist). Does the limit…

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Q: 2x f(x) x + 6 10 100 1,000 f(x) -5 -10 -100 -1,000 f(x) Use the results to guess at the indicated…

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Q: Show that the function f(x) = |x – 2| is not differentiable at 2. We have if x > 2 f(x) = |x – 2| =…

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Q: 15. Investigate In (x + 1) In (x + 999) lim lim and In x In x Then use l'Hôpital’s Rule to explain…

A: L' Hopital's Rule is used in the following cases,

Q: This question has several parts that must be completed sequentially. If you skip a part of the…

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Q: 1/(1+e^(1/x)) state the value of each limit. lim f(x) as x -> 0- lim f(x) as x ->0+ lim f(x) as x…

A: Given:  f(x)=11+e1/x

Q: 58. If f(xo, Yo) 3, what can you say about lim f(x, y) (x, y)→(xo, Yo) if f is continuous at (xo,…

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Q: 5. Prove that if lim g(r) = 0 then lim g(x) sin () = 0. %3D

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Q: 45. Suppose x. ifx 1/n for every natural number n, f(x) ={0. otherwise. b) Does lim, 0f(x) exist? If…

A: Given :f(x)=xx=1n ∀n∈ℕ0otherwiseTo check :limx→0f(x) exists?Formula :By Archemedian property ε&gt;0…

Q: 45. a) Find lim h(x). b) Find h(1). c) Is h continuous at x = 1? Why or why not? d) Find lim, h(x).…

A: Given Example -

Q: Q.No 3.) if x<-1 Let f(x)={ax+ B if -13x<1 x² +2 if x21 Find a and B, so that lim f(x) and lim f…

A: Given that, Consider, limx→-1-f(x) = limx→-1- x3 = (-1)3 = -1 limx→-1+f(x) = limx→-1+ (αx+β)=…

Q: and b at where? ] Use the &-8 definition of the limit to prove lim(4x-3)=5. X2 Find the & value When…

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Q: 6. Formally, we define a limit as follows: lim f(x) = L if we can prove that for every constant e >…

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Q: We determined that l'Hospital's rule applies to the limit  lim x→5   x2 − 10x + 25 x2 − 5x

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Q: 56. Let f(x) = [x] + [-x]. (a) For what values of a does lim,-f(x) exist? (b) At what numbers is f…

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Q: 2. Find the limit and confirm your answer using the sandwich theorem 1 - cos x lim 818 1. 2. 3. 4.…

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Q: -x + 1,x 2 0 Let f(x) = {x² + sin x -,x <0' (a) Find left-hand and right-hand limits as "x"…

A: Consider the given information:

Q: 2. find: en(x?) a). Lim メ-1 b). Lim 1 - cos "x 1-COS 4x2

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Q: ,if x> -3 Given the function f(x) =' 3 ,ifx S-3 is continuous at x=-3

A: A function                      fx=x2-9x+3,   if x&lt;-33,             if x≤-3 We have to answer the…