Given f(x) = x² + Va, then f(4+ h) – f(4) - a) lim h>0 h f(æ) – f(1) x – 1 b) lim Note: write either decimal numbers or fractions in the form a/b.

Q: Find the limits lim х2 — 1 as a. x→1+ b. x→1 c. x→-1+ d. x→-1

A: we have to find the limit    the given expression is

Q: If f(x)=2-3x². O a. O b. O c. lim h→0 lim h→0 lim 30 From first principles select the correct step.…

A: Given :fx=2-3x2

Q: Find lim f(x) if I-00 4x - 1 I 5.

A: NOTE: Refresh your page if you can't see any equations. . here we have

Q: Find the limit algebraically. ( f(-3 + h) – f(-3) lim h0 where f(x) = -3x2 + 2x + 9

A: Our objective is to find the limit algebraically.

Q: Given: limx→+∞ f(x)=4 limx→+∞ g(x)=3 limx→+∞ h(x)=-7 Find: limx→+∞ [f(x)+3g(x)] = ? limx→+∞…

A:

Q: 21 f(x)= 3x2 +4x +1 and g(x) = x2 -2x-3, then what is lim f(x) *→19(x)?

A:

Q: Use the graph to solve for z.* := lim f(r) 3 3 f(x) 2. 2.

A:

Q: IF FLX)= and Lim F(X)6 F(-)=2 b X<l Find a,b when X#0

A:

Q: What is lim f(z) z→1 9(2) given f(x) = e2" and g(x) 3x2 – 3x + 6 ?

A:

Q: Solve the problem. Given that f(x) = 5x², find lim [f(x) - f(4)/(x - 4)]. X-4

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 lim, » 1512i (z2 + 30z) = x + iy, what is the value of a

A:

Q: Evaluate in terms of the constant a.

A: We have to find the limit in terms of constant a: limx→02a+x This is determinate limit so we need to…

Q: x2 Given that f(x) where a and b %3D (x- a)(b- x) are natural numbers and a > b, find lim f(x). X-a

A: Givenf(x)=x2x-ab-xwhere a and b are natural numbers and a&gt;b.

Q: Use the equation f'(a) f(x) – f(a) to find f'(a) at the given number a. lim х — а x2 f(x) a = 6 1. x…

A: Given

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

A:

Q: Evaluate in terms of the constant a. lim (2a + x) x→ 0

A: To Determine:  Evaluate in terms of the constant a.…

Q: Given the function f(x) = 5x2 - 3x + 5, determine: f(z) – f(x) a) lim Z-X b) f(x)

A: Please refer the attached image for complete solution.

Q: If 3x – 1 0, find lim f(x). X→3

A: Given query is to find the indicated limit.

Q: Given: x + 1, -2 < x < 0 x = 0 0 < x < 2 x = 2 2, f(x) = -x, 0, 2 < x < 4 х — 4, What is the lim…

A: Consider the given function. fx=x+1,          -2&lt;x&lt;02,                x=0-x,…

Q: If 2x – 2 < f(x) < x² – 2x + 2 for x 2 0, find lim f(x). X-2

A: The objective is to find the limit.

Q: If f(x)=x2−9x−3 , what is limx→3+x2−9x−3 , limx→3−x2−9x−3, and f(3) ?   Is f(x) continuous at 3?

A: Given,              f(x) = x2 − 9x − 3

Q: Given the piece-wise function x² – 2x + 5, Зx2 — 2х —5 f(x) = 0 2 Find lim f(x) and lim f(x) x-2…

A:

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

A: Given that : as per squeeze theorem

Q: When the function f(x) satisfies f(1) =1,f'(1)= 3 obtain a value of lim/ (2)" -1 x→1 x² – 1

A:

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

A: Given

Q: If f(x) = 3x2 - 4x +1 and g(x) = x² + 2x - 3, then what is lim 9X, g(x). X-1 f(x)

A:

Q: Suppose p and q are polynomial functions. If lim p(x)/q(x) = 9 and q(0) = 3, find p(0).…

A:

Q: If 1/(x^2 + 1) ≤ f(x) ≤ 1 + x^2 for all x in the interval (−1, 1), what is lim x→0 f(x)?

A: Please refer the attached image for complete solution.

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 lim f(x) and lim f(x) for I-2 x² + 2x I < -2 Vr + 2 4x – 2 2<I f(x) = -2 < x < 2 -

A: Topic- limits

Q: If f(x) = 22 +1, then find lim f(x)-f(0)

A: Given, f(x)=2x2+1 ∴ f(0) = 0+1 = 1

Q: 18) Find lim f(x) %3D X 2 - A) – B) 2 00 C) 1 D) 4

A: Topic = Limits 18) B

Q: Find the limits. f(x) = 2x2 – 3x + 41, g(x) = Vx + 3 (a) lim f(x) X-4 (b) lim g(x) = (c) lim g(f(x))…

A: Given

Q: Let f(x) = Vx - 1 if x>4 and f(x) = x² – 4x + 1 if x < 4. Find: %3D lim f(x) x→4

A:

Q: Given: f(x) = 4 –x’ and g(x) = Vx+1 a. lim f(x) =

A: Given, fx=4-x2gx=x+1

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

A:

Q: Given f(x) = 4 – a² and g(x) = væ + 1, find lim g(f(x) 2

A: Given,     f(x)=4-x2        and     g(x)= x+1then, to find                 limx→1gf(x)=?

Q: If 8x – 19 < f(x) < x² + 4x – 15 determine lim f(x) x→2 What theorem did you use to arrive at your…

A:

Q: If f(x) = 4" , then lim %3D (A) 4 (B) ! 1.

A: f(x)=4xlimx→0f(x)-f(0)x-0=limx→04x-40x=00, indeterminate form. Apply l'hospital rule to simplify

Q: If p(x)=x²+2x -3 and q(x)=x3-1, then lim 3p(x) 4q(x) x+1 II

A:

Q: x+1 If f (x) : Solve to find lim f(x)? Vx2+5-x'

A: We find limit

Q: Forf (x) = 2x +2, compute lim ƒ(1+h) –f (1) %3D f(I+h) -f (1) lim h>0 %D h

A: Given : fx = 2x+2

Q: Find the value of lim f(x), if f(x) = x3+ 6x + 2 x 3

A:

Q: (b) Given that lim f(x) == 2 and lim g(x)=4 , find the limit x2 1 lim 3f(x)- Vg(x) x→2 Using the…

A: Given thatlimx→2f(x) = 2  and limx→2 g(x) =4    and we have to find the value of the limit…

Q: If 3x-35f(x) < x²-3X+6 for X z0, find. lim f(x)

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Q: Find the limits. f(x) = x + 3 g(x) = x2 (a) lim f(x) X→-1

A: A limit tells us the value that a function approaches as that function's inputs get closer and…

Q: Use the definition to show that x² - y² lim (x,y) →(0,0) x² - y² 0.

A:

Q: Given the piecewise function |x² + 1, if x > c f(x) = | 2æ, 2x, if x <c lim f(x) exists find the…

A: