Determine the general antiderivatives of the following functions: a. f(x) = 20x+ – 4x³ + 15x² – 14x – 9 %3D b. f(x) 3D 7х3— 11х2 — 2х + 8 с. f(x) %3D хз — х2— х

Q: Show that the differential form in the integral below is exact. Then evaluate the integral. (-2,4, -…

A:

Q: 4 1 T/2 Зл/2 -1 -2 -3 -4 -5 The graph of the function f(x) = cot x is given above for the interval a…

A: From the graph of f(x)=cot x, we have to find its asymptotes

Q: Evaluate the line integral along the path C given by x = 2t, y = 4t, where 0 <ts 1. x + 3y2) dy

A:

Q: Sketch the region R and evaluate the iterated integral F(x, y) dA. (1 - 2x + 8y) dy dx 2.0- 2.0 1.5…

A: A detailed solution is given below

Q: | (2x - y) dx + (x + 7y) dy. Evaluate C: x-axis from (0, 0) to (0, -7) and (0, -7) to (4, -7)

A: x-axis from 0,0 to 0,-7 indicates that interval of y is from 0 to -7 y-axis from 0,-7 to 4,-7…

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

A:

Q: Determine the generating function of the following sequence {0, 0, 0, 1, 1, 1, ....}

A:

Q: Evaluate the iterated integral. 1/4 y cos(x) dy dx

A:

Q: Peaive marima and, minima, 4 any tar the funchno If there is not an answers write N/A Wde ms wefs as…

A:

Q: 3. Find a set of symmetric and parametric equations of the line passing through the point (1, 4, 2)…

A:

Q: The marginal cost of producing the xth box of CDs is 90 + x + The total cost to produce 100 boxes is…

A:

Q: Match the vector field with its graph. F(x, y) = xi + 3yj -st

A: Plot the given vector Fx,y=xi+3yj.

Q: 2. Find an equation of the plane containing the point P (0,-.) and the line determined by the two…

A: Equation of a plane P containing a line of intersection of two planes P1,P2 is given by, P=P1+λP2

Q: Evaluate -5x lim,→0 tan x O -5 O 1 O 5

A:

Q: Activity 1.5.3. A company manufactures rope, and the total cost of producing r feet of rope is C(r)…

A: Given problem :- A company manufactures rope, and the total cost of producing r feet of rope is C(r)…

Q: .2 x dx 9 – 4x²

A:

Q: Evaluate the improper iterated integral. x2 dy dx 1 + y?

A: The solution is given in the next step.

Q: Consider the function f (x, y)=-2x'+3x'y+2 y°-9y+5

A:

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

A:

Q: 2. The volume of the sun is 1.4 x 10 cubic kilometers and the volume of the earth is 1.1 x 102 cubic…

A: Earth mass

Q: Determine the value of the Wronskian W (y1, Y2) of y" – 2y +1 = e2 (x +1) if x=1.3 by using…

A:

Q: Find V· (F x G), if F(x, y, z) = 10xi +j+7yk and G(x, y, z) = xi+ yj – zk. V · (F × G) =

A:

Q: Find V. (V x F), if F(x, y, z) = 3e"i+ 7xe"j – 3ek. V.(V × F)

A:

Q: ||r(t) x r"(t)|| Use the formula k(t) to find k(t). r(t) = 8 cos(8t)i + 8 sin(8t)j + 5tk к(€)

A:

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: 5x + 2lnx 8. lim X+3Inx

A:

Q: Verify Green's Theorem by evaluating both integrals ÔN I y? dx + x2 dy = dA ay ax 'R for the given…

A:

Q: Evaluate the line integral along the path C given by x = 4t, y = 8t, where 0 s t < 1. dy

A: Given: I=∫Cx+3y2dy And x=4t, y=8t  and 0≤t≤1   As we know that; The Power rule: ∫xndx=xn+1n+1+C

Q: Find V (F x G), if F(x, y, z) = 11xi +j+ 13yk and G(x, y, z) = xi + yj – zk. V. (F x G) =

A:

Q: Evaluate the triple iterated integral. xyz dx dy dz Jo

A: To evaluate the triple integral.

Q: Qu= O.4 log (E+0.44 435 %3D Qa - 0.249(log Ea)-O.I77 Q8= 0.227 (log E3)-0.839 Q3= rearange equations…

A:

Q: Find the coordinates of a point P on the line and a vector v parallel to the line x = 3 - 5t, y = -1…

A: This is a problem related to vector. Based on the general concept and formula we will answer the…

Q: The cumulative percent of sexually active boys ages 15 to 20 is given in the table. Complete parts…

A:

Q: Calculate the first eight terms of the sequence of partial sums correct to four decimal places. E…

A: We can solve as follows

Q: Solve the following differential equation step by step! y" – 2y' + y = x² + 1

A:

Q: ||r'(t) × r"(t)|| ||r(t)||³ Use the formula k(t) to find k(t). r(t) = 2 cos(4t)i+ 2 sin(4t)j + 9tk…

A: We have to solve k(t)

Q: Consider the function f(x) = 12x° + 30x4 – 300x³ +3. f(x) has inflection points at (reading from…

A:

Q: Evaluate et-2 lim x→2 _x – 2 1 O +∞ O 1 O -00

A: Use l hospital rule for finding the correct option.

Q: ntinuous function, f (x), has a domain of [-6, 6] -6 <x<-2 x=-2 -2 <x< 0 x=0 0 < x<6 does not exist…

A:

Q: Use Hooke's Law to determine the work done by the vaniable force in the spring problem. A force of 7…

A: The answer is 5.6 pounds

Q: Find the volume of the solid that results when the region enclosed by the geviN curves. -2X ソニ e;…

A: The given curves are; y=e-2x, y=0, x=0 and x=1. So, the bounded region is as shown below. Now apply…

Q: Find the curvature and the radius of curvature at the stated point. r(t) = 8 cos(t)i+7 sin(t)j+10tk;…

A: This is a problem related to vector. based on the general formula of curvature and radius of…

Q: Evaluate the definite integral. Using Fundamental Theorems of Calculus. π 1 sin -x cos? 1

A:

Q: dx a sin x+b cos x

A: Find integration of dx/ a sinx+ b cosx

Q: Describe the domain and range of the function. KX, y) = 9x2 - y

A:

Q: What is the volume of the solid formed by revolving the region bounded by the graphs of x2 = 7y and…

A:

Q: Verify Green's Theorem by evaluating both integrals dA Əx ay, or the given path. C: boundary of the…

A:

Q: Evaluate the triple iterated integral. r2 xyz dx dy dz

A:

Q: Determine whether the improper integral diverges or converges. In x xp O converges O diverges…

A:

Q: Зх -5 dx (x+1) (x+2)²

A: