5. For the function f (c) find the limits and the value. (14 points) f ()27 + 3, 2 c<2 (a) lim f(x) (b) lim (a) (c) f(2)

Q: Discuss the limit of the function as x approaches c and the value of the function as x = c.

A: The solution of above question is written in step 2.

Q: l'Hos pital's Rule to nd the exact value the limit. lim 9*-8* 3*-2*

A:

Q: x+2 x3 3

A:

Q: (7) Evaluate the limit of the function by determining the value the function approaches along the…

A: a) ley y=0L=lim(x,y)→(0,0)xy-y3x2+y2L=lim(x,0)→(0,0)0(x-02)x2+02L=0x2L=0b) Let…

Q: 3. Sketch the graph of a function y(x) with domain (-x, 0) that appears to satisfy each of the…

A: Given: The domain of the function is all real number,  limx→∞y(x)=5limx→-3y(x)=-∞limx→4y(x) does not…

Q: I. Find the limit of the algebraic functions if it exists. Show your solution analytically. 1.…

A:

Q: 1. Which mathematical expression corresponds to the statement "the limits of the function x2 + 2 as…

A: Since you have asked multiple questions, we will solve the first question for you. If you want any…

Q: Find the limit of 9x6 lim x + 1

A: limx→∞9x6-xx3+1 limx→∞x69-xx6x3+1

Q: The process by which we determine limits of rational functions applies equally well to ratios…

A: Given, limx→-∞x2+x-18x2-313

Q: 1-y+2,7-2,5 Q6) find the limit lim (xy)-(00)

A:

Q: C.2 show that the function even or odd or not 4-X 04Evuluut the fallowing Limits Lim メー」 メー」 2Lim…

A: Q. 3).

Q: Graph the function. Then use your graph to find the indicated limit.

A: Graph the function f(x)=1-x for the region x&lt; 0. Then graph the function f(x)=cosx for the region…

Q: 1. lim (x + 4) = 13 x>3 The limit of r + 4 as x approaches 3 equals 13. What does this statement…

A:

Q: The process by which we determine limits of rational functions applies equally well to ratios…

A: The given limit expression is limx→ -∞ 1-x3x2+7x5.

Q: 6. For the function h whose graph is given, state the value of each quantity, if it exists. If it…

A: As per the company guidelines we can solve first three subparts. I hope that the given solution will…

Q: 2. What is lim f(x)? lim f(x)? Why? 10+ 8- 6. 4+ 2 -10 -9 -8 -7 -6 -5 -4 -3 -2 -1 4 1 2 3 4 5 6 7 8…

A: Given: The graph of fx as To find: limx→0+fx and limx→0+fx

Q: Given that: lim f(x) = 5 x-2 lim f(x) = -5 x--3 lim g(x) = -1 x--2 lim g(x) = -10 x--3 Apply the…

A: To find limx→-38fx+9gx

Q: Find the number a such that the limit exists. 3x2 + ax + a + 6 lim x2 + x - 2 X--2 a 18 Find the…

A: To find  The number a such that the limit exists.

Q: The process by which we determine limits of rational functions applies equally well to ratios…

A: To find the limit  limx→-∞4-3x3x6+9

Q: 1. For the function ƒ whose graph is given, determine the following limits. 3 lim f(x) X2 -6 -5 -4…

A: A limit of a function at a point exists if at that point the left-handed and right-handed limit…

Q: 2. The limit lim 10х — 2 -

A:

Q: 2. Find the limits. Use L’hospital's rule where necessary. Not a calculator problem! x' – 7x? +10x…

A: (i) L=limx→2x3-7x2+10xx2+x-6=00 Now Apply L'hospital rule…

Q: Determine whether the statement makes sense or does not make sense, and explain your reasoning.

A: lim x→4fx = 0lim x→4gx = 0To verify:          lim x→4fxgx ≠ 0   is correct or not.

Q: The process by which we determine limits of rational functions applies equally well to ratios…

A:

Q: Determine if the following piecewise-defined function is differentiable at the origin. 7x- 2x - 12,…

A:

Q: d the indicated limit given that lim f(x) = 5 and lim g(x) = 4. x-a xa lim [2f(x) – 4g(x)] xa

A:

Q: 6. If f(z) = 4 then lim f(x)- 12

A: Using limit ,

Q: lim f(x) = 5 x--2 lim f(x) = -5 x→-3 lim g(x) = -1 x--2 lim g(x) = -10 x--3 Apply the properties of…

A:

Q: 1 Let F (x) = 1 +2 2< Find lim F (x). 2+

A:

Q: .If I want to evaluate f(-1) what value do I get? If I want to 2. In our first week we are learning…

A:

Q: when at x=a, f(a) is a real number. The function assumes an indeterminate form when x=a, both the…

A: 1) this is true. 2) this is also a True.

Q: (3х + 3с if x >2 Let f(x) = {x2 - cx if x < 2 If lim f (x) exists, find the value of c. X-2

A: Limit of a function exist , when both sided LHL and RHL exist.

Q: 2. Given the graph (on the right) of y = f(x). Find the following limits, if they exist. (1) lim…

A: (2) Consider the given graph as

Q: . Discuss the limit of the function as x approaches c and the value of the function as x= c.

A: Limit of  function is the most important part of calculus. Suppose f(x) be any function with…

Q: xample: Using the Sandwich theorem 1. If V5- 2x2 <f(x)< v5– x² for -1< x< 1, find lim f (x)

A:

Q: (x+1 4. lim f(x) = {(x - 4)2 +3 if x <4 if x 24 ズ→1

A: Given: fx=x+1, if x&lt;4x-42+3, if x≥4 To Find:  To determine limx→1 fx, then to graph the function…

Q: 2) Use the graph of f to estimate the following limits. No work needs to be shown for this…

A: To evaluate the limits with the graph.

Q: 1. Without a table of values and without graphing f(x), give the values of the following limits and…

A:

Q: Evaluate lim(4+ x). x2 x 2 Input from the f(x) or y Output from the the left right side right side…

A: fx=4+x When x=0, f0=4+0=4 When x=1.5, f1.5=4+1.5=5.5 When x=1.99, f1.99=4+1.99=5.99 When x=1.9999,…

Q: 13. (a) Estimate the value of lim- X x+√1+3x-1 X √1+3x-1 By graphing the function f(x) = - (b) Make…

A: Given: 13. f(x)=x1+3x-1 To find: (a) Value of limx→0x1+3x-1 by graphing f(x)=x1+3x-1 (b) A table of…

Q: 3. What is lim f(x)? lim f(x)? Why? X-0 AY 10 8 6. 5 -4 -3 -2 2 5 3. -1

A:

Q: 36. f(x) - 8 x-2x²x2 If lim = 3, find lim f(x) x-2

A: As per our company guidelines, we are supposed to answer only the first question, please repost…

Q: 7. Find the limits if they exist using the graph below. y = f(x) 2. a. lim f(x) b. lim f(x) x 2-…

A:

Q: A portion of the graph of the function f (x) = /x is -3 shown to the left. We are examining the…

A: Given:   f(x) = x  ;    at x=2⇒ f(2)=2    Also given that: limx→2…

Q: Find the limit of (x^2)/((2^x)-1)) as x goes to 0.

A: To find :  limx→0x22x-1

Q: 2. Given the graph (on the right) of y = f(x). Find the following limits, if they exist. (1) lim…

A: 2) From the graph we can see that (i)  limx→0+f(x) = -4limx→0-f(x) = -4 Hence limx→0f(x) = -4   (ii)…

Q: The graph of f(x) passes through the point (4, 0). The slope of the line tangent to the graph at the…

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.