37. Give an example where lim (f (x) + g(x)) exists but neither lim f(x) nor lim g(x) exists.

Q: Find the limits limx→0+{1 + 1/x}x

A:

Q: 2) Show that the_lim. 1) xy2 lim (x,y)→(0,0) x² +y²

A:

Q: Prove from the precise definition of a limit: lim x = 4 x-2

A: We have to solve the limit using definition.

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

A:

Q: lim (4.x – 3) = 9

A: The given limit,      limx→34x-3=9

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

A:

Q: lim x² ln x x-0*

A:

Q: Estimate the limit numerically. x² lim +14x+49 -7 x+7 O-7 Oto∞ O-1 00

A: Given limit is We will use the factorization method to evaluate the limit By using the result that…

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

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

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: Prove using formal definition. (a) lim x→0+ 1/x = ∞.

A: Draw the graph of the function .

Q: Find the limit of the function lim x → − 6 ( 2 x + 12 | x + 6 | )

A: Find the limit

Q: x² – 1 lim x→1 x – 1

A:

Q: Find the limit. 3x + 5 lim x→0 x - 4

A: Find the limit  limx→∞3x+5x-4

Q: (b) Prove that lim,→20,¤€A ƒ (x) exists and is equal to lim→0 Yk-

A: This problem is related to the sequence of functions. Given:  fkk∈ℕ is a sequence of functions from…

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→0 x – 1

A: Given that: limx→∞5x-1

Q: Find the limit. lim (2 – x)7 tan(=) x→1

A: It is asked to evaluate the given limit. For solving the problem we need to know some basic…

Q: Show by example that lim[f(x) +g(x)] can exist even if lim f(x) and lim g(x) do not exist.

A: Let,  f(x)=1x-c, g(x)=1c-x

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

A:

Q: Find the indicated if it exists: lim x to +infinity;  2x2+3x+1 divided by x4 - x2

A:

Q: Calculate the limit.

A: Calculate the limit.

Q: Investigate the one-sided limits graphically:

A: We have to investigate the one-sided limit graphically of the following function -  limx→0+ ln x

Q: If Lim [x3 – g(x)] = 12 as x tends to 3, use the Rules of Limits to find Lim g(x) as x tends to 3.…

A: Given: limx→3x3-gx=12

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

A: Topic:- calculus

Q: 4. Using the precise definition of a limit, prove lim (2x +8) = 38. x-15

A:

Q: 4) Determine the limit. lim 1 f(x), where f(x): X + 10 X-- 10-

A: Given, f(x)= 1/(x+10)

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: 3. Find the limit of +2x+3 lim X-2 V x+5

A: As per Bartleby guidelines, we will solve only first question To find the limit of limx→2x2+2x+3x2+5

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

A:

Q: Show that 2 x² - y² - 1 lim (x,y) →(1,0) 1 − x + (2y)² - does not exist.

A:

Q: Use the formal definition of a limit to show lim (2x + 1) = 5. x+2

A: Given: limx→2 2x+1=5

Q: find the lim as x approaches infinity when f(x)= (1-x)/2x

A:

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

A: Given: fx=x2-4x   limx→0fx+x-fxx=?

Q: lim(4x – 3) = 5 x→2

A:

Q: Evaluate the limit 5 + 2x lim 8 – 8x x → 0

A: We haven the function is: f(x) = (5 + 2x)/(8 - 8x)  Dividing the numerator and the denominator by x…

Q: Evaluate the limit. lim X→∞ 5 (₁ + 2/2 + 1/2)² X

A:

Q: Compute the indicated limit. „2 x + 3 lim x00 x - 4

A:

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: c) lim -4e-x

A: c) limx→∞-4e-xlimx→∞-4ex

Q: Use continuity to evaluate the limit. lim In(2 + V1 + x)

A:

Q: Suppose that lim as x approaches infinity of f(x) + x^2 = L for some number L. Then lim as x…

A:

Q: Find the specified limit. f(x) - x+2, x > -1 lim f(x) ?

A: The given function is            f(x) = x2,  x&lt;-1x+2, x&gt;-1 We have to find the following…

Q: 2/ Find the limit of the function lim X415 хъ Ч 2 X

A:

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

A:

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

A:

Q: Find the limit. lim etan x x-(9x/2)+

A: We have to find the given limit

Q: Find the limit x lim- +x+2 X + x +1

A: