Assuming that lim x→a f(x)/(x−a)2 exists, find lim x→a f(x)/x-a

Q: evaluate the limit lim x→1+        (ln(x)) / ( ln(x − 1))

A: Given:

Q: If x3 f(x) s x for x in [-1,1], find lim f(x) if it exists. X-0

A:

Q: Find the limit (if it exists). If it does not exist, explain why.

A: Given: gx=1-x,       x≤1 gx=x+1,          x>1 The limit limx→1+gx is the right hand limit at…

Q: What is lim1 f (x) ? X

A: Find your answer below

Q: Use the Squeeze Theorem to find limx→c f(x).

A: Given that 4-x2≤f(x)≤4+x2 To find the limit of the function using the Squeeze theorem when x→c=0.

Q: lim x² ln x x-0*

A:

Q: Evaluate the limit. lim  xe3/x − x x → ∞

A: We have to find limit of f(x).f(x) is given below:

Q: Prove that limxc f(x) = Lis equivalent to limxc [ f(x) − L] = 0.

A:

Q: What is lim f(x)? X-1

A: Given graph: To Find: limx→1f(x)

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: Compute

A: The limit of the function is the value of the function when the value of the arguement is…

Q: Find the limit.   Lim  x→1+      x1/1-x

A: Given function is By property of logarithm

Q: Find Limit Using Squeeze Theorem: 2. If 2x – 2s f(x)<x² – 4x + 3 for x 2 0, find lim f(x).

A:

Q: If −x2 − x + 1 ≤ g(x) ≤ x2 − x + 1 for all x does not =0, what is lim x→0 g(x)?

A:

Q: Evaluate the limit: -V4+x² lim X→0- x2

A: limx→0--4+x2x2

Q: Let F(x) = (x2 + 3x + 2)/(2 - | x | ). Make tables of values of F at values of x that approach c =…

A: Given: Fx=x2+3x+22-x To determine: We have to estimate limx→-2Fx by making a table of values of F at…

Q: Find the limit. . lim 2x²-x-3 X-1 x+1 . lim 2+h-vZ x-5 E lim x-5+ x2-25 . lim o. f (x) = fx³ +3 lx -…

A:

Q: Lim X-0 √1+x-√1-x x

A: evaluate the limit limx→01+x-1-xx

Q: lim -1 x→0+

A: Separate the limit.

Q: V2x -1 Using defination of limits, prove that lim Jx- 3 L^ = x4

A:

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

A: solution is given below..

Q: Is there a value of a for which limx1 3x^2+ax+a+3/x^2+x-2 exists? Enter the value of a if such a…

A:

Q: If f (x) = −x + 8 for x ≤0 and f (x) = 4x + 7 for x > 0, find (a) limx→0+ f (x) (b) limx→0− f (x)

A: We can find the limit as below.

Q: X- Zx +3x+2 lim

A: Solution of question as follows

Q: If 2x+2 ≤ f(x) ≤ x2 +2x+2, for all x, then find lim f(x) x-> 0

A: Given

Q: V2x –1 Using defination of limits, prove that lim Vx- 3 L^ = X4

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

A:

Q: Using the ɛ, & definition, prove that lim V = 1. %3D x 1

A: We have to prove the given limit.

Q: Find the limits limx→1+x1/(x-1)

A: limx→1+xx-1

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: Use lim f(x) = -2 and lim g(x) = 5 to find the limit. %3D lim [3f(x) – 4g(x)]

A: The given limits are limx→cf(x)=-2 and limx→cg(x)=5

Q: Find the limit: limx 1(x2 + x + 2)/( x + 1)

A:

Q: Find the constant c so that the limit limx->3 (x2+x+c)/(x2-5x+6) exists.

A:

Q: Find the limit. (a) lim x→3 Vx +6 – x x3 – 3x2

A:

Q: Find limx∞ h(x), if it exists, f(x) = 5x3 − 3…

A: Given: fx=5x3-3

Q: determine the limit limh→0[(x+h)2-x2]/h by treating x as a constant. determine the limx→0cos(2x)/x…

A:

Q: show that lim(x,y)→(0,0) (x^3+xy^3/x^4+y^2) does not exist.

A: We will see that along y=mx2 path limit does not exist which means limit does not exist.

Q: Find the limit. /x² +3 - 2 lim X- 1 X1

A:

Q: c) lim -4e-x

A: c) limx→∞-4e-xlimx→∞-4ex

Q: use f(x) to find: limx→0f(x), limx→-4f(x), limx→5+f(x), limx→-4-f(x). the discontinuity that is…

A:

Q: f(x) is discontinuous at x=c, then  limx→c-  f(x) ≠ limx→c+ f(x) True or False?

A:

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: Evaluate the limit. x2 + 2x – 15 lim- x – 3 X-3

A:

Q: |x| does not exist. Show that the limit lim x 0 X

A: Given: limx→0xx

Q: lim(x,y)->(0,0)  (4x2y)/(x2+y2)1/2

A: Given: lim(x,y)→(0,0)4x2yx2+y2         (1) To compute: The limit.

Q: Find the limit. lim(v² + x = x) = lim( Vx2 + x – x

A:

Q: Use numerical evidence to estimate the value of the limit to at least 2 decimal places. x² + 2x - 48…

A: Solution: