Application of derivatives Questions and Answers

In the country of United States of Heightlandia the height measurements of ten year old children are approximately normally distributed with a mean of 55 3 inches and standard deviation of 2 9 inches A What is the probability that a randomly chosen child has a height of less than 57 85 inches Round your answer to 3 decimal places B What is the probability that a randomly chosen child has a height of more than 60 1 inches Round your answer to 3 decimal places Answer Appuer

18 Evaluate the expression Arccos A 1 B Arccos cos C 3 D

23 What is the period of the graph of y csc x A 2 B 4T C 3 D T

15 Given cose 3 A 2 B C 34 55 5 3 5 which is in quadrant II find Si

A B C D 9 chy one period of the graph of the equatio art at

1 Find the solution set of each equation in the interval 0 x 2 4 cos 2x 2 A 1 1 1 6 6 B T 57 77 117 6 6 6 6 C 3 3 D TT 5m 3 3

Find the open intervals where the function f x x

49 Given A 24 25 B 200 25 C 244 D 24 7 sine 25 which is in quadrant I find csce OF

Find the open intervals where the function f x

32 Evaluate the expression tan sin 1 5 13 cos 3 5 A 33 56 B 11 12 C 13 D 15 65

41 What are the extreme values of y sin x 6 TT A and 3 B 1 and 1 C 6 and 6 D 75 and 75

46 Find the amplitude of the following equation Y 1 3 cos 4x A 3 B 1 3 C 4 D 12

sin 65 50 Reduce 1 cos 65 to a single function of one angle A tan 32 30 B tan 130 C cot 32 30 D cot 130

44 Evaluate the expression Sin A H TT 4 B C 3TT 3TT D 71 4 I 2 2

TT 29 The period of the graph of y cos x 7 is A B 2 T C D

34 Find the inverse of y 5 A y 5 B x 5 C y 15 D x 5

TT 38 What is the variation of this function y cos 0 2 to A Increases from 0 to 1 B Increases through all negative values to 0 C Decreases through all positive values to 1 D Decreases from 0 to 1

37 What is one identity you could use to convert the LHS csc ecose to cote 1 A csce sine 1 B cote tane C CSC e I cose D cose csc e

28 Given A B II Find the values of the following sin 2A 12 25 C 1 D 7 25 sin A 24 25 4 tanB 7 24 angle A is in Quadrant I and angle B is in Quadrant

33 Given tane 1 A 2 2 5 B 2 C D 48 N 2 which is in quadrant II find sece

Part 2 of 2 Find the open intervals where the function is concave upward or concave f x 3x x 6 Where is the function concave upward and where is it concave downward A The function f is concave downward everywhere VB The function is concave upward everywhere

16 Find the exact value of sin 165 A 6 1 4 B C 6 4 2 6 2 4 D 6 2 4

19 Find the exact value of cos 195 A V6 1 B V6 4 2 C V6 2 4 D 6 2 4

22 Evaluate the expression A V B 2 C 2 D 3 sin Cos 1

25 Give the size and direction of the phase shift of the second equation relative to the first equation y 4sin 4x y 4 sin 4x 5 A B C D 3 to the left 12 to the right 12 to the left TT 3 to the right

23 What is the period of the graph of y csc x A 2 B 4 C 3

8 Find the solution set of each equation in the interval 0 x 2 cos 2x sinx 0 A 0 B C Flo 6 6 FIN Fl6 FI3 D 5T 3T 66 2

TT 11 Give the extreme values of the function y 5 cos x 7 A 1 and 1 B and C 5 and 5 D and

18 Evaluate the expression Arccos A 1 B 13 Arccos cos C 3 D

tan 44 tan 16 1 tan 44 tan 16 What is the value A 3 12 B 3 C 3 D 3

14 What are the extreme values of y 2cos A 1 and 1 B 3 and 3 C and 3 2 D 2 and 2

9 Given cose A B ma alw C 4 D 3 3 which is in quadrant II find cote

5 Express the product of 2cos30cose as an algebraic sum A cos 300 cos 30 0 B cos 30 0 sin 30 0 C cos 30 cos 30 0 D cos 30 0 cos 30 0

7 Evaluate the expression cos Cos 7 12 A 2 B C 1 2 D 2

For each of the sequences below enter either diverges if the sequence diverges or the limit of the sequence if the sequence converges as noo Note that to avoid this becoming a multiple guess problem you will not see partial correct answers A B 4 C 4n 8 n D 4n 8 n sin n 4n

The composite bar in figure is firmly attached to unyielding supports Compute the stress in steel caused by the application of the axial load P 35 kips A B C Aluminum A 1 35 in 2 E 10 x 10 6 psi 12 in 15 483 23 psi 30 192 31 psi 12 589 45 psi Steel A 1 95 in 2 E 29 x 10 6 psi P 8 in

A bronze bar is fastened between a steel bar and an aluminum bar as shown in figure Axial loads are applied at the positions indicated Find the largest value of P that will not exceed an overall deformation of 3 5 mm or the following stresses 150 MPa in the steel 130 MPa in the bronze and 75 MPa in the aluminum Assume that the assembly is suitably braced to prevent buckling Use E 200 GPa E 70 GPa and E 83 st al br GPa 2P Steel A 480 mm A 8 000 N B 2 0 m D 36 000 N C 4 500 N 24 000 N Bronze A 650 mm 3P 4P 3 5 m Aluminum A 320 mm 3 0 m 3P

A 2 5 in diameter steel tube with a wall thickness of 0 10 inch just fits in a rigid hole Find the tangential stress if an axial compressive load of 4580 lb is applied Assume v 0 45 and neglect the possibility of buckling A 1862 15 ksi B C 2624 15 psi 1862 15 psi

Find the volume of the prism whose base is the triangle in the xy plane bounded by the x axis and the lines y x and x 1 and whose top lies in the plane z f x y 3 x y

4 marks Show that the equation xy 1 z e 1 defines z as a function f of x and y in a neighbourhood of a 0 0 2 marks Sketch using Matlab or otherwise the graph of f in a neighbourhood of a

Find a degree 3 p 1 Write Pin expa

Add 6 81 sum m Subtract 6 81 difference Question Help Messa Calculator

0 mplify each of the following ar 9 36 2

nd all zeros real and non unction including factors fo nter the zeros separated b

For Graph A L3 16 and R3 23 For Graph B L3 17 and R3 10 Compute error bounds for L3 and R3 for both figures The error bound for L3 and R3 for Graph A is Simplify your answer Ay 16 14 12 10 8 6 4 2 0 ON Ay 16 14 12 104 8 6 4 2 0 0 y f x 12 2 12 4 6 Graph A y g x 4 6 Graph B 8 8 00

Which of the rectangles below are left rectangles Ay 254 20 15 10 51 A BCD EX 0 0 5 10 15 20 25 OU Select all of the left rectangles below A Rectangle D B Rectangle A C Rectangle E D Rectangle C E Rectangle B F There are no left rectangles

Is y 14x a solution of the diff The function y 14x

Find the amount A in an account after t years given the following conditions dA dt A 0 8 000 A t 0 01A

For a person learning to type the number N of words per minute that the person could type after t hours of practice was given by the limited growth function below What is the rate of improvement after 6 hours of practice After 40 hours of practice N 101 1 e 0 02t What is the rate of improvement after 6 hours of practice words per minute per hour of practice Round to the nearest hundredth as needed

M Find the value of t for which the logistic function given below is equal to 2 y M 1 Ce kMt