2. Find the area of the region bounded by y =x-1and y 3– x. Sketch the graph. Hint: Use vertical rectangular strip or element.

Q: 5 8. Let f(x) =-x + 4 cos 3x. On the interval 0 < x< 2n, what is the average height of the function?…

A: A detailed solution is given below

Q: %3D What is the area of the region bounded by the graph of r = 4 sin 20? Choose two (2) correct…

A:

Q: Preview Activity 1.5.1. One of the longest stretches of straight (and flat) road in North America…

A: Given problem:- Preview Activity 1.5.1. One of the longest stretches of straight (and flat) road in…

Q: Consider the following equations. f(x) = x5 + 3 %3D g(x) x + 3 %3D

A: The region is bounded by the graphs,  fx=x5+3 and gx=x+3

Q: Activity 1.5.2. A potato is placed in an oven, and the potato's temperature F (in de- grees…

A: Solution: Given data

Q: Laplace transform of (t+2)^2

A:

Q: ||r(t) x r"(t)|| Use the formula k(t) = to find k(t). ||r"(t)||° r(t) = t'i+ t°j K(t) =L

A:

Q: Evaluate the line integral along the path C given by x = 2t, y = 4t, where 0<ts 1. (y – x) dx +…

A: Just I have used the given parametric representation of the curve C to change the given line…

Q: Evaluate lim,-(-- 7 - 10 + 4) | 4x3 O +∞ O -7 O -10 8.

A:

Q: Find T(t) and N(t) at the given point. r(t) = 11 cos(t)i + 11 sin(t)j + tk; t= -11 /122 T(5) V122 0,…

A: Given: r(t)=11cos(t)i→+11sin(t)j→+tk→ r'(t)=d11cos(t)dti→+d11sin(t)dtj→+dtdtk→…

Q: mal places as needed.)

A:

Q: The height of a right circular cone is always three times the radius. Find the volume of the cone at…

A:

Q: Evaluate lim, (-5x + 5 – 5 - ) 12 O + O 5 O-5

A:

Q: Find div F and curl F if F(x, y, z) = 3y°z©i – 3x*z°j – 3xy*k. div F= curl F=

A:

Q: 1+ cx, if x 2 Given the function: f(x) = C - x, What should be the value of c so thatf is…

A:

Q: Find volume of the solid obtained by rotating the bounded region determined by curves y = In x, y =…

A: We have to calculate volume of solid obtained by rotating the region bounded by y=lnx, y=0 and x=2.…

Q: -6 Evaluate , (2x + V) dx. A. 27 + 2/3 + 4/6 B. 27 2/3 C. 27 23 4V6 D. 27 + 4v6

A: The objective of the question is evaluate the definite integral and choose the correct option . Here…

Q: use the definition of the derivative to compute f'(x) given f(x) 3x+2

A:

Q: 2) Find of the following equation then simplify whenever possible. and dx dx2 x = 1+ Sin t y = Cos?…

A: The given parametric equation,   x=1+sin t, y=cos2t

Q: Consider the function f(x) = 2x° – 15x? – 36x + 8 on the interval [– 5, 9]. Find the average or mean…

A:

Q: se Hooke's Law to determine the work done by the variable force in the spring problem. A force of 9…

A: Given is the question of hooks law.

Q: Use the method of cylindrical shells to find the volume generated by rotating the region bounded by…

A:

Q: Evaluate the following limits. If needed, enter INF for oo and MINF for -oo. (a) lim (Va + 3r +1-1)=…

A:

Q: Evaluate the iterated integral. T/4 '5 y cos(x) dy dx

A: A detailed solution is given below

Q: On the axes below, make an appropriate scale and graph exactly one cycle of the trigonometric…

A: Here, the given function is: y=7cos(8x) Note that the period of the function is: 2π8=π4 Now, the…

Q: Use Green's Theorem to evaluate the integral. Assume that the curve Cis oriented counterclockwise.…

A: Given:        ∮C7xydx+4xydy  Where C is the rectangle bounded by x=-1, x=2,y=1 and y=5  The formula…

Q: Find the vector v with the given magnitude and the same direction as u. Magnitude Direction ||v|| =…

A:

Q: Solve

A:

Q: Use Green's Theorem to evaluate the line integral. y2 dx + xy dy C: boundary of the region lying…

A: Given problem:-

Q: 4. Find the equation of the tangent line and normal line that passes through the circle (x – 2)² +…

A:

Q: At 10:17 a.m., you pass a police car at 55mph that is stopped on the freeway. You pass a second…

A: Here, note that the distance between two police cars is 39 miles and the time between them is…

Q: What is the differential equation whose solution represents the family y = Ae3x + Be 3x+Ce4x? %3D O…

A:

Q: Find div F and curl F if F(x, y, z) = xz°i+ 2y°x²j+2z²yk. %3D div F= curl F=

A:

Q: Find the area of the following region bounded by the graph of f(x) = (x - 5) and the x-axis between…

A:

Q: write the equation of the tangent to the Eunction: 2(x? +y=J%=25(x* -y^) at the point (3, 1) %3D

A: First we calculate the slope of tangent at the given point

Q: 1. Suppose you are in charge of payouts for a competitive 10K race. You decide that the top 12…

A: (A) Solution:  In both options total amount is same i.e. $546,000 but option B situation will be…

Q: Evaluate the line integral / (4x + 8y)d.x + (4x – 9y)dy along the curve C : x = 10 cos t, y = 20…

A:

Q: If we apply Rolle's Theorem to the function f(x) = 2x2 – 16x – 4 on the interval [2, 6], how many…

A: We state Rolle's theorem here ------    Let f : [a,b] -&gt; R be a function continuous on [a,b] and…

Q: Verify Green's Theorem by evaluating both integrals aM y? dx + x² dy = | / (G dA ay əx for the given…

A: Solved below.

Q: r In x 2

A:

Q: Of all rectangles with a perimeter of lo meters, which one has the maximum area? (GIve both the…

A:

Q: Match the equation with its graph. 16 56

A:

Q: d'y Find dx? 2 y = (2а-3)? dy 48 dx? (2г - 3)" O dy -12 da? (2г- 3)" O d'y 12 dx? (2a-3) dy -8 da?…

A: y=2(2x-3)2

Q: Use Green's Theorem to evaluate the integral. Assume that the curve C is oriented counterclockwise.…

A: Explained below

Q: ...... ... ... ...- Evaluate the iterated integral. 5. y cos(x) dy dx

A:

Q: Determine the vector field of F. F(x, y) = 8i – 4j

A:

Q: For the function g whose graph is given, state the following. (If the answer is positive infinite,…

A: As per our guidelines we are supposed to answer only first three parts. Kindly repost others…

Q: Find curl (5z i+ 6x j+ 7y k). curl(5z i+ 6x j+ 7y k) = ( i )i + ( i Oj + ( i )k Savo for Lator

A:

Q: Evaluate the integral (8x + 12y)dx + (9x – y)dy along the parabolic (8x +12y)dx + (9x – y)dy along…

A:

Q: / Va2 – 1 ¢2 – 1 dx

A: