2t – 2 t2- 1, Let r(t) = - î - tan (t) ĵ+ In(2t) k. %3D (a) Determine the domain of r. (b) Compute lim 7(t). t+1 dr (c) Compute dt

Q: Given f(x) = 3 (4-a)3 Evaluate lim→4-f(x) Select one: O A. 0 B. -00 C. +0 D. -1 E. Does not exist

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Q: X-3 lim y→3+ Vx2¬-9 х2-9

A: Find the limit of limx→3+x-3x2-9

Q: (a) Let r(t) = (√√t² – 1, e¹t, ln(2t — 4)). (i) Find the domain of r(t). (ii) Find lim3 r(t). (iii)…

A: Step 1:Step 2:Step 3:

Q: Consider the function f defined by 1²+y² V12+y?+1-1 ,2 f(r, y) = %3D lim(7.y)¬(0,0) f(x, y) =

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Q: of discon tinuity of the the following func Hions (a) g(x,y) = stuind %3D (b) b) f laiy)

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Q: f(x + h) - f(x) For the function f(x) = 5x? + 12z + 32, find f'(x) using the definition Jim %3D h O…

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Q: Suppose f(t) = 5t² + t + 3. Evaluate: lim f(t) = t→-2

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Q: Q1. Find the domain of the functions f(r) = V(2 -1)(r -7) and g(r) = In(r² – 4)(3-r). Also determine…

A: Solution:-   fx=2-x x-7                           & gx=ln x2-4  3-x      Find determine the…

Q: 1 — х b. lim х36 (х — 6)2

A: b) limx-6(1-x) /(x-6) 2 a) limx-5 (x-1 sqrt(3x+1))/(x-5).

Q: x³f(2)-24 If f(x) is differentiable at x = 2 and lim,-2 = 28, then f (2) = %3D x-2 Select one: О а.…

A: B correct

Q: A particle is moving along a horizontal line according to the function: s(t) = 4t2 + 1, where t is…

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Q: t² + 1 t 1 %3D lim→1- h(t) = ?

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Q: Find the domain of r(t).

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Q: Let f(x) = -√√√x6 + 14 + x³ +1. Complete the tables below. Round all table values to four decimal…

A: The given function .The aim is to find the function value at the given points and find the limits…

Q: f(3+ h) – f(3) (4) 7. For f(r) = x² – 4x + 5, determine lim h0 h (6) 8. Consider the curve defined…

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Q: Consider the function f defined on the domain -0.5 s x s 0.5 with f(0) = 1, and 0.5 lim h 0 f(x+h)-…

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Q: (c) lim v f(x) x→2

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Q: domain

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Q: If f(x) = (3x – 2)10 , then f(1 + h) – f(1) lim h→0 h О 15 O 5 o 7.5 O 10 O 30 O 20

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Q: Q2. Find the x² + y² lim (x, y)→(0, 0) √√x² + y² + 1 − 1

A: We have to solve above question and find  limit

Q: B. Calculate the limits of the following functions.. 1. limx¬-1(2X2 + X + 4) 2. limy--2(y3 + 5y – 1)…

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Q: Suppose that f(x) = Ax² + Bæ. Find the values of the constants A and B if f(2) = -4 and %3D…

A: We have to use definition of limits.

Q: 2. For h(t)= Vt +12t – 2r² evaluate each of the following limits. (a) lim h(t) (b) limh(t) 『→の

A: We will find out the required limit.

Q: (b) lim h 30 у49 + h - 7

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Q: (d) fof(2)= (e) lim f(x)= x→0 5f(x) (f) lim x+3 || =

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Q: Let fn(x) = n²x²(1 – x) on [0, 1]. Does lim,-00 So fn(x) exist?

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Q: t3 + 8 . tan(t + 2) Let F(t) j+ (t* – 1) e“-4k , find lim F(t). t+2 t+2 t-2

A: Limit of a vector point function

Q: For the function f(x) = 7x2 + 12x + 32, find f'(x) using the definition lim f(x + h)- f(x) %3D h->0…

A: