(a) Let r(t) = (√√t² – 1, e¹t, ln(2t — 4)). (i) Find the domain of r(t). (ii) Find lim3 r(t). (iii) Find r'(t).

Q: f(x,y) = e (3x² + 3y2)

A:

Q: 10х? + 11ху + y .2 lim +,9) ->(-1,10) 10х2 — 39ху — 4у2

A: Introduction: If a function f(x,y) of two variables x and y, is continuous at the point (a,b), if…

Q: (c) h(x, y) = 1 In(9x² - y2)

A: c Given that, The function is hx,y=1ln9−x2−y2.   Domain:- The domain is the set of input values for…

Q: (c) lim →1 是 æ-1 1 T-1 = 3.

A:

Q: Find lim √√3x² + 3y² -1. (x,y) →(3,1) lim √√3x² + 3y² -1 = (x,y) →(3,1) (Type an exact answer.)

A:

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

A:

Q: f(x)=√x −7 lim h→0 f(6+h)−f(6)/h

A: Question is solved.

Q: пу-1 lim y→0_2y² y(e2™y–1)

A: To evaluate limy→0(πy(e2πy−1)+πy−12y2) Rewrite the given expression:…

Q: The time t in hours, employees are on the working on assembling widgets. The employee rate of change…

A:

Q: Find lim (x,y) →(7,0) 7x - 5y #49 √7x-5y-7 7x - 5y-49 by rewriting the fraction first.

A:

Q: (A) f(x) = √√√x + 2x (B) f(x) = √√√x – 2x² (C) f(x) = 2x² + √x (D) f(x) = 2x − √√x

A:

Q: Find lim v² + 2x – x. (а) 0 (b) 1 (c) 2 (d) o (e) DNE

A:

Q: domain

A:

Q: lim b→∞ 2x 22 x² + 1 -b dx.

A: To solve the following problem of integral and then find the limit

Q: df-1| For the function y = f(x) = x + 3x + 1, > 1.5, find dy (f-)'(3) = %3D

A:

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: **. (1) lim,- V1+cos 2x 4 (x-) Q3) Find:

A:

Q: k lim (1+†) k→∞ k

A: We have to find limit

Q: x° +2y² +x*y lim (* ,y') → (0, 0) x* +3y - x*y

A:

Q: 4x2 – 2 8х — 4 f(x) = f'(x) =- (х — 1)2 (х — 1)3

A: Given the function fx=4x2-2x-12 Domain of the function:- y=4x2-2x-12 x-1=0⇒ x=1 Domain x≠1 So,…

Q: consider the following function: f(x)=cos(2-2x)

A: The given function .The aim is to find the period of the function.

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: Find F(s). F(s) = L {tu(t = 3)}

A: detailed solution is given below

Q: Find all the asymptotes of y -8xy +15x +13x – 3y+ 2=0.

A: Given equation is  y2-8xy+15x2+13x-3y+2=0

Q: Use FunCtion 9(x) = - f (X)tZ gra ph Of Y = fLX) to g raph Y=F(x) 2十 -4

A:

Q: Let f(x)=3−x2. Find each of the following: a) f(−1)−f(−6)−1−(−6)=  b) f(−6+h)−f(−6)h=  c)…

A:

Q: 1. lim (2r + 5) 2. lim (10 3x) X12 3. lim(-x + 5xr 2) 4. im (x'-2r? + 4x + 8) 5. lim 8(t - 5)(t-7)…

A: