6. Consider the following function. 5-x x<-1 f(x)%3D -15x<5 (x- 5)2 x25 Determine the values of a for which lim f(x) exists.

Q: 1. Let f(x) = 3² – 2x + 1. Compute lim (x)f – (4 + x)f 0+-4

A:

Q: 2. Draw a function with the following criteria: lim f(x)=2, f(-5)=-4 X-5 lim f(x)=0, lim…

A: Answer

Q: 1. Complete the following tables of values to investigate lim (x2 – 2x + 4). x→1 f(x) f(x) 1.6 0.5…

A:

Q: 11. If f(x)=Vx f(x)-f(4)| The lim x→4 х-4

A: Given: fx=x To Find:  limx→4fx-f4x-4=?

Q: Vx+15 -2 is The value of the limit lim X+-11 x+11

A:

Q: lim V3x² – 6 X-2

A: The given problem is,           limx→23x2-6 Here the function is continuous and defined at x=2, so…

Q: 3x lim x→0 x2 + 2x

A:

Q: Consider the function x + 1| – |x – 1| f(x) Estimate |x + 1| - |x – 1| lim x 0

A: The given function f(x) is:

Q: 1. Evaluate the limit for the graph lim f (x). x→1" f(x) 51 4- 3 2 1- -3 -2 -1 1 2 3 4 -1 а. 1 c.…

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

Q: Determine the following limits: 2x +3 [a] lim b lim 0 4x-4 sin x

A:

Q: Find the limits x² - 7x lim X-o X + 1

A: Given: limx→∞x2-7xx+1

Q: Evaluate lim as x approaches negative infinity 3e^2x + 4e^-x / e^2x - 2e^-x .

A: Limit of a function determines the continuity of a function. Three types of limits exist, one is…

Q: 2x+1 if x 2 Determine the one-sided limit lim f(x). x-2- 2

A: The given function is:

Q: Vx-2 lim х+4 х-4

A: To evaluate: limx→4x-2x-4

Q: If you know in advance that lim f (x) exists, can you determine its X+5 value from a plot of ƒ for…

A: Given that limit of f(x) exists at x=5.That means the function f(x) is continuous and differentiable…

Q: Q.4: Prove or disprove, lim f(x) = 4 If f(x) = x # 2 x = 2' I-2

A:

Q: (4) Consider the function + 3bx + 262 if x 1 For which value(s) of b does lim f(x) exist? Justify…

A: Given: fx=x2+3bx+2b2             if x&lt;1 fx=x-1                             if x≥1 limx→1fx…

Q: 12. Given f(x)=x² – 4x – 5. Find lim fx) –{2) x-2 2

A:

Q: 2. Consider the function: + 3 if x 2 %3D 17 if x = 2. %3D Find lim, 2 f(x).

A: Function given is- f(x)=x2+3       if x&lt;2x3-1      if x&gt;217           if x=2  To find…

Q: 16. If f(x) = 2x – 1, what is lim x+h h B. - С. —2 D. 2 NIN

A:

Q: If 3x s f(x) sx +2 for 0sxs 2, evaluate lim f(x).

A:

Q: 2. lim (e* – 1)lnx X0+

A:

Q: 4. Evaluate the limits of the following functions: a) limsinx x-0 sin x-tan x 6 b) lim x-2 x2+2x-8)…

A:

Q: Find the limit of the function lim x → − 2 ( 2 − | x | 2 + x )

A: Topic:- calculus

Q: i. Calculate the following limit: 2x|x – 1| lim - x-1 x-1 ii. Determine the limit of f(x) when x…

A:

Q: 2x-1 2. lim X-2 \3x+4,

A:

Q: 3. Is lim f(x) always equal to f(c)?

A: Is limx→cfx always equal to fc The given statement is not necessarily true.

Q: 4. Given that f(x)=4x - 3 f (1+h)- ƒ(1) Find lim ,x21

A: Given query is to find the value of indicated operation.

Q: Suppose that following is true. x2 + 6 if x s 0 if 0 <x < 1 f(x): 7x² - 6 if x 2 1 What is lim f(x),…

A: Just compute right hand limit and left hand limit and see if they are equal or not.

Q: 4. What is the sign of a if f(x)= ax' +x +1 satisfies lim f(x) = 0? x→-0

A: Given that fx=ax3+x+1 satisfies limx→-∞fx=∞. Note that the given polynomial having odd degree.

Q: lim (In 2x + 5) + 4 X→ー1

A: Solution:limx→-1ln2x+5+4=ln2-1+5+4

Q: Evaluate the following limits if they exist x +5x-3 a) lim x² + 2x – 6 x² – 3x – 1 b) lim x' +1 c)…

A: In the question we have to calculate the limit of the following functions given.

Q: Show that the function given below is continuous. 4v2 - 16v lim -2 v-4

A:

Q: The function values for h(x) near x = 1 are given in the table below. -0.10–0.05–0.011 2.01 2.05…

A: Given

Q: lim -2)2 x-2 x2-4 3.)

A:

Q: 3. Find the following limits: x2 +5x +6 (a) lim x-3 x2 + 4x + 3 Vx2 + 5x +7 (b) lim 5 – 2x (c) lim…

A: As per our guidelines, we can not solve  more than 3 subparts so please repost  the remaining  part…

Q: x² +1 if x -1

A:

Q: 2. Find the following limits. Do (a) and (b) without a calculator and (c) and (d) with a calculator…

A: We have limx→0x-4x+4=limx→0x-4limx→0x+4=0-44=-42=-2

Q: Q.4: Prove or disprove, lim f(x) = 4 If f (x) = } x # 2 x = 2 x→2 2.

A:

Q: 10- In parts (A)-(C), find the indicated quantity for y = f(x) = 5- x. f( - 1)- f(- 2) (A) (-1)-(-2)…

A: Given the function simple put the value of (-1) and (-2)  find the value of y and put it on that…

Q: 3. If f and are continuous functions with f(3) 4 and lim 2f(x)-9(r)3D5, what is g(3)?

A: To evaluate the value of the function

Q: —ах+6 if x2-1 Let f(x)=< For what value of a does 2x2 +ах ifx<-1 lim f(x) exist? x--1

A:

Q: If V5 - 2r s f(x) < V5 - x for -1 sxs 1, find lim, 0 f(x).

A: Given: 5-2x2≤f(x)≤5-x2

Q: Find the following limits. √x-3 X-9 x-9 1. lim t²-7t+10 2. lim- t-2 t-2 3. A function f(x) satisfies…

A: Since, you have posted multiple questions, as per guidelines, we"ll solve only first three…

Q: Find the following limits. x²+3x-4 x -16 1. lim 2. lim X-1 X-1 x+2

A: Apply the limit to the given expression and if it results in 0/0 form then take the derivative of…

Q: 6) Find lim f(x). X>T/2

A: Given graph we have to find limx→π2f(x)

Q: * :Test the following function using limits x² - 25 lim x→→5 x² + 2x - 15 B) 5/3 A) 5/4 O C) 5/2 O

A: Apply the following steps to find the value of the given limit. Factorize the expressions in the…

Q: What conclusion about f(x) can be drawn from the equation lim-a+f(x) = f(a)?

A: Given that limx→a+f(x)=f(a)

Q: -10 2468 10 x -4+ ad • +8- -10- Find lim f(x) = %3D

A: The graph of the function f(x) is

Q: Evaluate the following limits. 2. e* + e-*-2 a) lim b) lim (1 +2x) 3/ 3/x x2 c) lim x2 In x x-0*

A: Hey, since there are multiple questions posted, we will answer the first question. If you want any…