f(x + x) – f(x) lim x 0

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

A:

Q: Suppose that lim 4f(x)+ 2x – 14 5. Find lim f(x). z→1 %3D z→1 x – 1

A: Given

Q: find the limit of g(x) as x approaches the indicated value. 3x2 + 1 lim = X g(x)

A:

Q: Find the limits a) lim x2 - 4x + 3 x2 - 1 when x approaches 1 b) lim 6x + 100 7x2 100 when x…

A: We have to find the limit

Q: If 3x - 4 s f(x) sx2 - 3x + 5 for x 2 0, find lim f(x). x-3

A: Given, 3x-4 ≤ fx ≤ x2-3x+5              for  x ≥ 0 We have to find limx→3fx

Q: Consider f(x)=x−9/x+4 a) As x→∞, f(x)→ b) As x→−∞, f(x)→ f(x)=10x+7/x−6 c)limx→∞f(x)=

A:

Q: If / 10 - 7x2 sf(x)s/10 – x² for - 1<x<1, find lim f(x). lim f(x) = x→0

A:

Q: If 3x < f(x) < x³ + 2 for 0 < x < 2, find lim f(x). x-1

A:

Q: Find the limit L.

A: We have to find the limit L: limx→4x+2 This is determinate form of the limit so we need to put limit…

Q: Find the limit L. 2x + 10x + 8 lim X→-4 x + 4 L =

A: Solution-

Q: If Зx <f(x) < х +2 for 0 <x< 2, find lim f(x). х—1

A: Result used:

Q: Find the indicated limit if it exists. √x+4-2 a) lim X-0 X 8x³+27 b) lim x-1.5 2x + 3

A:

Q: Find lim f(x) for the given piecewise function. x-4 2x +2 if x 4 If the limit does not exist, enter…

A:

Q: Let f(x) = x² + 9, x > 0. Find lim f'(x) →25

A: f(x)=x2+9

Q: If 2x – 1 < (x) <x² for 0 < x < 3, find lim f(x)

A: The solution of above question is written below.

Q: If lim as f(x)-4/x-3=2 as x approaches 5, find lim f(x) as x approaches 5.

A: We have

Q: Find lim f(x) for the given piecewise function. X6 2x + 1 if x 6 If the limit does not exist, enter…

A:

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: If 2x - 1 0, find lim f(x). X→2

A:

Q: Find the limit. lim x→3 1−x2/(x-3)2

A: Given, The limit limx→3 1-x2x-32  We have to find the limit.

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

A: Given function is By property of logarithm

Q: If 7-6x2 sf(x)s 7-x² for -1sxs 1, find lim f(x). X→0 lim f(x) =

A: If 7-6x2≤f(x)≤7-x2 for -1≤x≤1, we have to find limx→0f(x)

Q: Find lim h(x), if it exists. f(x) = 7x2 + 2x + 3

A:

Q: Lim X-0 √1+x-√1-x x

A: evaluate the limit limx→01+x-1-xx

Q: Find the limit L.

A: Given: L=limx→4x2+6

Q: If 2x 0, use the Squeeze Theorem to find lim g(x).

A: Given that : as per squeeze theorem

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

A:

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

A: Given

Q: Find the limits 1 lim x→0 x²/3

A:

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

A: Topic:- calculus

Q: Find the limits limx→1+x1/(x-1)

A: limx→1+xx-1

Q: If 5-4x sf(x)s5-x for - 1<xs1, find lim f(x), lim f(x)%= f(x) =D

A:

Q: If 3x – 2 s f(x) < x² - 3x + 7 for x 2 0, find lim f(x). X3

A: 3x-2≤f(x)≤x2-3x+7

Q: find the lim as x approaches infinity where

A:

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

A: Given: fx=5x3-3

Q: If 2x - 2s f(x) S x² - 2x + 2 for x 2 0, find lim f(x) x-2

A: see below the answer

Q: Find Lim as attached. f(x) = x2 − 4x

A: Given: fx=x2-4x   limx→0fx+x-fxx=?

Q: If 3x – 2 s f(x) sx² - 3x + 7 for x2 0, find lim f(x). x-3

A:

Q: If /10 - 7x sf(x)s/10 -x for -15xs1, find lim f(x). x-0

A:

Q: if Væ² – 5x – 6 < f(x) – 1 < v6² – x² then find lim f (x) - | - x-6

A: Given:x2 - 5x -6  ≤ f(x) -1 ≤ 62 - x2To find : limx→6f(x)

Q: If 3-2x sf(x)s3-x for -1sxs1, find lim f(x). lim f(x) =|

A: Calculate left hand limit and right hand limit than find the limit using sandwich theorem.

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

A:

Q: Let flx)= S2x-1 if x>3 what is lim f(x) ? 2x+2ifX<3, what is lim flx)? メ-3 とラメふとす

A: Given: fx=2x-1if x&gt;3x+2if x≤3

Q: Find the limit of the function algebraically. x2 + 2x lim

A:

Q: Suppose f(x) = x2 if x ̸= 2 and is undefined at x = 2. The domain is (−∞,2)∪(2,∞). Find lim f (x).…

A: The limit exists at x tends to 2 for f(x). First of all, consider the condition for the limit to…

Q: Q2: Use lim x 0 and lim x 0 to show that lim x = 0.

A:

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

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.