Verify that the equation is exact then solve it. (axy-sec²x) dx + (x²+2y)dy = 0 You may use the calculus III or the DE method.

Q: Determine the equation of the line perpendicular to the tangent line to the function y = ecosx at…

A:

Q: The following limit represent the derivative of a function f at a point a. Find a possible f and a,…

A: let function is f(x) given is derivative f'(x)=limh→0(1hsin2(π4+h)-12

Q: Find the curvature of the curve r(t). r(t) = (2+ In(sec t))i + (6 + t)k, -л/2 < t < π/2

A: We need to find curvature of curve.

Q: Using known power series, find the Taylor series of f(x) = e-x² + cos x centered at a = 0 and state…

A:

Q: Decide whether or not the functions are inverses of each other. 1 f(x) = 5x + 25, g(x) = x-5 No O…

A: fx=5x+25 gx=15x-5 fgx=f15x-5=515x-5+25 fgx=x-25+25 fgx=x

Q: When a cold drink is taken from a refrigerator, its temperature is 5°C. After 25 minutes in a 20°C…

A:

Q: The average worker at Wakefield Avionics will have assembled N(t) = −4t3 + 24t2 + 4t (0 ≤ t ≤…

A: Given that , Nt=-4t3+24t2+4t , 0≤t≤4 How many hours into this shift is the average worker performing…

Q: Evaluate (3x + 3√Y) ds where C is given in the accompanying figure. √(3x + 3√y) ds = (Type an exact…

A:

Q: A rectangle is inscribed between the x-axis and the parabola y = 12 - 2² as shown in the figure

A: Let point of rectangle of x axis = ( x , 0) Therefore, Point on curve (x , 12-x2)

Q: Convert the point (r, 0, z) = (6, 7, 4) to Cartesian coordinates. Give answers either as…

A:

Q: Example 1 The function F(x) = x6 is an antiderivative of f(x) = x5 since F'(x) = f(x).

A:

Q: INTEGRAL CALCULUS 7. Find the area bounded by the parabolas: x² 4y and x² = 8y - 4.

A: x2=4y..........1    f(x)=x2/4 x2=8y-4............2   g(X)=x2/+4/8

Q: bok 2 K F2 Graph the function y = 4x²+3x-1 by identifying the domain and any symmetries, finding the…

A:

Q: A company determines that its marginal revenue per day is given by R'(t)​, where R(t) is the total…

A: Here we have  R'(t)=90et, C'(t)=90-0.5t

Q: A company makes three sizes of cardboard boxes: small, medium, and large. It costs $1.50 to make a…

A: Number of small boxes=xNumber of medim boxes=yNumber of large boxes=z

Q: Given the tangent to y = lnx is y = its equation. at (e, 1). Find a parallel tangent to y = e* and…

A: Given that the tangent to y = lnx is y=(1/2)x at (e,1).  Here we have to find a parallel tangent to…

Q: Find the curvature of the curve r(t) = (4 cos(3t), 4 sin (3t), 2t) at the point t = 0 Give your…

A:

Q: Find the curvature of the function Y 1 at x = 2. Find the radius of curvature at x = = 2.

A:

Q: Find the length of the curve 7 (t) = (3 cos (5t), 3 sin(5t), t) for -6 ≤ t ≤ 4 Give your answer to…

A: We have given a vector function and we have to find the length of curve.

Q: Match the exponential function with its graph. 1. f(x) = -3² +4 2. f(x) = 2x + 4 3. f(x) = eª – 3 4.…

A: 1. f(x) = -3x +42. f(x) = 2x +43. f(x) =ex -34. f(x) =-ex -3

Q: Express the equation in exponential form (a) log₂ 8 = 3. That is, write your answer in the form 24 =…

A:

Q: Verify whether the following equations are exact. If possible, solve the equation. y a) dx- - 2 X +²…

A: (a) xx2-y2dx-yx2-y2dy=0(b) 2x+6x2ydx+3y2+2x3dy=0

Q: Consider the followin gdifferential equation: y + 2 t+1 dy dt Find the general solutions and the…

A: “Since you have posted a question with multiple sub parts, we will provide the solution only to the…

Q: )Solve the I.V.P. xy' = 2y + x³e y(1) = 1

A:

Q: A medical researcher believes that the human immune system produces antibodies to a particular…

A: We have given a rate of production of antibodies in human body. We have to find the function that…

Q: ASIC Compute R6, L6, and M3 to estimate the distance traveled over [0, 3] if the velocity at…

A: Reimenn sum of integral

Q: (4) (a) Find the open intervals on which the function is increasing or decreasing. g(x)=27x-x³ (a)…

A:

Q: Evaluate the following limit using L'Hospital's rule. limx→0+ (e9x+6x) (1/2x)

A: To evaluate the following limit by using L'Hospital's rule. limx→0+e9x+6x12x

Q: Given the vector function 7 (t) = ( − t, - 2t³, − 5t³ + 1) Find the velocity and acceleration…

A: Vector field is given as, r→(t)=&lt;-t, -2t3, -5t5+1&gt;   We have to find velocity and acceleration…

Q: If the rational function y=r(x) has the vertical asymptote x = 6, then as x→ 6+, either y → (smaller…

A:

Q: A cylinder is inscribed in a right circular cone of height 4.5 and radius (at the base) equal to 8.…

A: We have given radius and height of cone. We have to find the radius and height of cylinder which has…

Q: Use the appropriate methods to solve the following integrals. a. So 0.5x e te e2x dx

A:

Q: Describe the given region in polar coordinates. R:srs.sos (Type exact answers, using x as needed.) C

A: Figure

Q: 7. Consider the following graph of a function. For what values is this function differentiable?…

A: Function non differentiable 1. when vertical tangent exist on graph2. On a sharp point 3.…

Q: Evaluate the given integral by changing to polar coordinates where R is the region that lies to the…

A:

Q: 16. Of all numbers whose sum is 340, find the two that have the maximum product. A. 10 and 330 B.…

A: Let one number be x and the other number y, then                x+y= 340       ⇒  y=340-x…

Q: Find the length of the curve a(t) = et cos(t), y = et sin(t) for 0 ≤ t ≤ 2. Give an exact answer,…

A:

Q: Use an appropriate change of variables to evaluate the integral 1. I = when D is the region in the…

A:

Q: Given the following velocity function of an object moving along a line, find the position function…

A:

Q: Σ(4) Does this series converge or diverge? converges diverges Given the series n-1 If the series…

A:

Q: The total cost incurred in operating a certain type of truck on a 500-mile trip traveling at an…

A: The total cost incurred in operating a certain type of truck on a 500-mile trip  traveling at an…

Q: Find the total area bounded by the x-axis and the curve y = f(x) on the indicated interval. Enter…

A:

Q: Work. An open tank has the shape of a right circular cone. The tank is 5 feet across the top and 20…

A: Work = Distance*density*volumeVolume of…

Q: Evaluate. (Be sure to check by differentiating!) x5 2 In x² dx, x>0 (Hint: Use the properties of…

A:

Q: The Taylor polynomial P(x) about 0 approximates f(x) with error En(x) and the Taylor series…

A: The solution is shown in step-2

Q: All units in a 100-unit apartment building are rented out when the monthly rent is set at r =…

A:

Q: Determine where the given function is concave up and where it is concave down. 10x x2 + 49 5) f(x) =

A: Given function,   f(x)= 10xx2+49The function f(x) is concave upward on an interval I if second…

Q: In a town whose population is 3000, a disease creates an epidemic. The number of people, N, infected…

A:

Q: (2) Show that f(x) = e³x cos(2x) is of exponential order.

A:

Q: Determine whether the series converges or diverges. 00 77 +1 6-2 n=1 The series converges by the…

A: The series is given as , ∑n=1∞7n+16n-2 Determine whether the series is converges or diverges.