Consider the function f(x) given by the graph below. y f(x)

Q: f(x+Ax)- f(x) Using the first principle of derivative f'(x) = %3D Ax Ax-0 Differentiate: y 4x - 6

A: Derivative of the function

Q: CSC X lim (secx t tans scx

A: To find the limit by using L-hospital rule L-hospital rule is  For limit(x tends to a) f(x)/g(x)…

Q: Rearrange lim x* so that we can apply L'hopital's rule. *→0+

A: Follow the steps.

Q: Use L'Hopital's Rule to evaluate the exact value of lim(x² – 2x+1)*-1.

A:

Q: 3) If the lim f(x) = 2 and lim f(x) = -1 %3D x-3- x-3+ Then what is the lim f (x) = x→3 %3D a) Why?

A: To find the limit of the f(x) at x=3

Q: to if iz fx) < x (x)_ +4x+4,for allx, find Lim f(x)

A:

Q: -|x|, h(x)=20-x², 4x-1, A) lim h(x) = x-5+ B) lim_h(x) = X115 C) h(3) = x≤-5 -5 3

A:

Q: 1. lim→- Зx? (2х - 1) 1 + 4x + 3 9. limx--3 x2- 3 2.

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Q: Use L'Hôpital's rule 3. x3 x³ - 1 lim x1 x³ + 3x - 4

A: limx→1x3-1x3+3x-4

Q: f(x)-f(7) B) If f'(7) = 5 then find the lim x+7 Vx - V7

A:

Q: 1.0 1.0 -1 ction f (x) : shown above. (x – 5)(x – 8)² does not exist, Þut is neither o ner -o.

A: Given function

Q: 9x²-7 If f(x) = what is limf(x)? Use a strategy OTHER THAN a table approach, a graphical approach,…

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Q: Let f(x)=x²+3 ifx<1 3x+1 ifx21 lim f(x) b) d) lim f(x) lim f(x) ƒ(1) Find

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Q: ل بريال

A: From the graph of given function

Q: f(x + Ax) - f(x) f'(x) = lim %3D Ax Ax-0 Differentiate: f(x) = x² + 4x - 3 CHOICES: (Just type ONLY…

A: Using given first principle of derivatives

Q: 1-x 6. lim X-3 X+3

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Q: find the lim as x approaches infinity where

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Q: How would you define f(2) in order to make f continuous at 2? limx→2 x^3-8/x^2-4 show ALL of your…

A: Let's solve limit problem.

Q: evaluate using the identity a^3 − b^3 = (a − b)(a^2 + ab + b^2)

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Q: TT. J V lim_x²e-5x x→∞

A:

Q: (sinx -) (3sin²x -sinx +1) lim TE +X, 2

A:

Q: 2. Consider f(x)=x² – 4x + 2 a) lim f(x) x-2 b) lim f(x) x-4 c) lim f(x) We X-1

A:

Q: Is there a function f such that limx→1 f(x) = 0 and limx→1 f(x) (x-1)³ = -∞?

A: To find:- A function f such that limx→1fx=0 and limx→1 fxx-13=-∞

Q: Match the correct boxes lim, 2-f(x) = 8 and lim-2+ f (x) = 8 lim, 2-f(x) = 6 and lim 2+ f(x) = 8…

A: The condition of existence of limit at

Q: Find limx→2−  f(x) Find limx→2+  f(x) Find limx→2  f(x) Find f(2)

A:

Q: limx → 1 (x-2) / (x-1)2 ii.  limx → 1 (x2-1) / (x-1) iii. limx → 1  |x-1| / (x-1)

A: