Let r(t) = (4sin 21)i + (4cos 2r)j– (e“ )k, be the position of particle in space at time . Find the velocity, speed and acceleration of the particle at -0. Problem 2: (2 marks) A projectile is fired from the origin over the horizontal ground at an initial speed of 900 m/sec and a launch angle of 600 (i) When and how far away will the projectile strike? (i) How high overhead will the projectile be when it is 9 km downrange. Problem 3: (2 marks) Find the curvature for the curve r(t) = (6sin 2t)i + (6cos 2t)j+ 5tk

Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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Problem 1: (2 marks)
Let r(t) = (4sin 21)i + (4cos 2r)j- (e“)k, be the position of particle in
space at time . Find the velocity, speed and acceleration of the
particle at t=0.
Problem 2: (2 marks)
A projectile is fired from the origin over the horizontal ground at
an initial speed of 900 m/sec and a launch angle of 600
(i) When and how far away will the projectile strike?
(ii) How high overhead will the projectile be when it is 9 km
downrange.
Problem 3: (2 marks)
Find the curvature for the curve
r(t) (6sin 2t)i + (6cos 2t)j+ 5tk
Problem 4: (2 marks)
By considering different paths of approach, show that the
following function has no limit.
9x*y
lim(.y)-(0.0)
7
9x.
V5
Problem 5: (2 marks)
aff
Let f(x, y) = sin(2.x) – y² In(xy- 3). Prove that dxây
дудх
Transcribed Image Text:Problem 1: (2 marks) Let r(t) = (4sin 21)i + (4cos 2r)j- (e“)k, be the position of particle in space at time . Find the velocity, speed and acceleration of the particle at t=0. Problem 2: (2 marks) A projectile is fired from the origin over the horizontal ground at an initial speed of 900 m/sec and a launch angle of 600 (i) When and how far away will the projectile strike? (ii) How high overhead will the projectile be when it is 9 km downrange. Problem 3: (2 marks) Find the curvature for the curve r(t) (6sin 2t)i + (6cos 2t)j+ 5tk Problem 4: (2 marks) By considering different paths of approach, show that the following function has no limit. 9x*y lim(.y)-(0.0) 7 9x. V5 Problem 5: (2 marks) aff Let f(x, y) = sin(2.x) – y² In(xy- 3). Prove that dxây дудх
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