2. Find a formula for f that satisfies the following conditions: lim00 f(x) lim-3- f(x) = 0, 0, lim-of(x) = 0, lim3+ f(x) = -0, lim+0f (x) = -00, f(2) = 0

Q: Determine whether the function x2 + 2 x > 2 f(x) = x = 2 is continuous at the 4х — 2 x < 2 given…

A: First of all we will find the left hand limit at X equal to 2 and then find the right hand limit X…

Q: 4-If. 2-x < flx) < 2Cos(x) for all x then find: lim f(x)

A:

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

A: Consider two functions fx &amp; gx By algebra of limits, we have, 1. limx→a fx+limx→a gx=limx→a…

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

A:

Q: 4. Is it possible that there exists some function g(x) and some constant L such that lim g(x) = lim…

A: First we need to understand definition of limit:

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…

A:

Q: b) If x sin x 2 - 2 cos x hold for all values of x close to zero. Find limx0 xsinx ? 2-2cosx

A: Given, limx→0xsinx2-2cosx

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

A:

Q: Let f(x) = x/(x + 1). What is lim, »f(x)? How large does x have to be so that f(x) > 0.99?

A: Given:            fx=xx+1 Find: limx→∞fx=limx→∞xx+1

Q: f(x) - If lim x--2 x 1, find %3D lim f(x) f(x) b. lim X--2 а. X--2

A: Given, the limit is                   We have to answer the given questions.

Q: a. Find the Domain for y = = /4 -x + ! b. For what value of (k) is the function y-f(x) continuous at…

A:

Q: 1. Determine whether the function f(x) = x2 + 6x + 9 is continuous at x =-= Sketch its graph…

A: Consider the provided function and the point, fx=x2+6x+9,   x=-2 Evaluate the provided function at…

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

A: The given function is:

Q: a. Evaluate limx→5 f(x), where f(x) = { 11x+ (2 +77) Ef x5 f(x) exists.

A: solution is given below..

Q: 3. Find the indicated limits. if x 2 f(x) -2+ 4x – x² a) lim f(x) x→2+ b) lim f(x) x→2- c) lim f…

A:

Q: -1, x0 c. lim f(x), where f(x) =

A:

Q: given f(x) = (x + 2x^3)^4 show the function is continuous at x = -1 by computing a.) f(-1) and b.)…

A:

Q: Q1/ Find the following 1. lim x2 + 1 = 2 x00 (x-2)2 2. lim x-2 (x-2)(x+2) 3. lim (5 -) x-0

A:

Q: Given that lim f(x) X+ 0 x2 1- explain why lim f(x)= ∞, x2 +7f(x)- sin (5x)+ 1 2- evaluate the limit…

A: We have to find the following

Q: 8-3x, for x <1 For parts b) and c), let f(x)= %3D x+x, for x21' b) lim f(x) x→1

A: We have to evaluate  limx→1- f(x) For x &lt;1 , f(x) = 8 - 3x

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

A:

Q: 5. If lim f(x) = 8 but lim f(x) does not exist, what can you X+2+ X+2 say about lim f(x)? X2-

A: We know that, limx→afx=l, if: limx→a+fx=limx→a-fx=l

Q: Find a formula for a function f that satisfies the following conditions. lim fx) = 0, lim f(x) - -0,…

A: Function

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: what is the lim x->0  f(x)-f(0)/x^2 if f(x)=2x^2+1?

A:

Q: 1/x, if x – 1 С. 1/x, if x – 1[ %3D X- -1

A: c) f(x) = 1/xx≤-1x2-2x&gt;-1limx→0f(x) = limx→0(x2-2) = 02-2 = 0-2 = -2

Q: 1. Determine the lim f(x) if f(x) : = {x*. if #2 lo, if x = 2 2. Find lim f(x) if f (x) = 2*

A: (1) Given that, f(x) = x2 ; if x is not equal to 2 f(x) = 0 ; if x = 2 Then we get, As x -&gt; 2,…

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: Let ƒ(x) = (x2 - 1)/( | x| - 1). Make tables of the values of ƒ at values of x that approach c = -1…

A: Make tables of the values of ƒ at values of x .

Q: Find the limit. lim (2 – x)3 tan(a) x→1

A: limit

Q: Find the limit L. Vx - 3 1 lim X 4 X- 4 L =

A: After the substitution of limits the function gives an indeterminate form 00.

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: 1 Let f(x) =. 1,0sx<2 .Determine lim f(x) -x² + 4x – 3, x 22 X2+

A:

Q: 3. If f (x) = (x² – 1, if x 3 3.a) lim f(x) X-3 3.b) lim f (x) 3.c) lim f (x) X-1

A: The given function is f(x)=x2-1,if x&lt;3x+5,if x≥3

Q: lim f(x)=+0, then the limit lim [2² . f(x)] .. If must be equal to zero. must be equal to +00. must…

A:

Q: x² +1 if x -1

A:

Q: Let: cos² x +1 f(x) Determine: lim f(x), lim f(x), lim f(x). and X- Specify horizontal and vertical…

A:

Q: x - 2x What is wrong with applying L'Hôpital's Rule to lim x+0 3x – 2

A:

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: The function f(x) of the below graph is discontinuous at x = -1 because: a) f(-1) does not exist b)…

A:

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: b. Is lim (x sin x) = lim f(x)g(x) = lim f'(x) lim gʻ(x) = ( lim 1)( lim cos x) = 1 a true or false…

A: Let we need to determine this limitlimx→0(xsinx)

Q: Consider the function - x2, x+1 f(x) = 2, x = 1 O Graph the function f(x). O Find lim,1-f(x) and…

A:

Q: 2. a) Find lim g(x), lim g(x) and lim g(x) x→1- x→1+ x→1 b) Find f(1). c) Is g continuous at x = 1?…

A: Follow the procedure given below.

Q: Determine a reasonable estimate for lim hx x-1 3 -5 -4 -3 -1 3 5 2. 1 4. 1. 1. 2. ee

A:

Q: 1. Determine whether the function ƒ(x) = x² + 6x +9 is continuous at x = -2. Sketch its graph…

A:

Q: 2f(x) + 3x – х — 1 15 - Suppose that lim 5. Find lim f(x).|

A:

Q: What type of discontinuity is at x = 3, if lim f (x)= 0 and lim f (x)= 0? x-3 x>3* What type of…

A:

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…

Q: b. For what value of (k) is the function y=f(x) continuous at x-3. x3-3x2-4x+12 x + 3 x-3 f(x) = %3D…

A: