Plot the curve r = 1+sin 8. Then find the length of the curve.

Q: Find the derivative of 83-4 A. 3 ln 8 B. 83x-4 C. D. OA OB OD OC 83-4 ln 8 83x-43 In 8

A: We are authorized to solve only one question, please repost remaining questions Derivative of…

Q: a. b. ² (30e³P +/- ¹ dp р 4 1 2 2x4 dx

A:

Q: 1. Find the area of the region enclosed by the given curves. a) y - x² = 2x and x + 4 = y b) x = y¹,…

A:

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

A:

Q: Find the critical number of the function defined by f(x) = x² + 4x O-1 and 0 are the critical…

A:

Q: 1 x² + 8x + 5 x3 + 12x2 + 15x + 6 dx

A: Solution of given question is written in below steps.

Q: ∫(2 cos(x) − 7sinx(x))dx   Evaluate indefinite anti-differentiation

A:

Q: Find the arc length L of the graph of r(t). L: = r(t) = 10 cos(t)i + 10 sin(t)j + tk, 0≤t≤ 2π

A:

Q: Find the volume generated by revolving about the y-axis the area bounded by the curve x^2 = 4(x-y),…

A:

Q: dx Find given that dt 6x² + 7y² = 13 x = 1, y = -1, and Give your answer as a simple fraction. dx dt…

A: Let us consider an expression, ax+by=c , a,b,c are constants. Then by implicit differentiation on…

Q: Ultrasound is often used to make images of developing fetuses. In particular, by measuring the size…

A: Given query is to find the rate of change.

Q: Find the domain of r(t) and the value of r(to). NOTE: Round your answer to two decimal places when…

A: We have to find the value

Q: Find T(t) and N(t) at the given point. r(t) = 6 cos(t)i + 6 sin(t)j + tk; t = T() 6 37 0, √/3 X N…

A:

Q: (8x4 − 5x2 + 2)dx evaluate indefinite anti-differentiation

A:

Q: dw the functions w= -5x²-3y².x= cost, and y=sint, express as a function of t, both by using the…

A: Use chain rule for derivative

Q: Use Green's Theorem to evaluate the line integral a-x)dx + (2x - x) d for the given path. C:…

A:

Q: Question 9 In MN = In M + ln N Maybe False True None of these

A:

Q: 3) Find the following derivatives: a. y = 2x b. f(x) = 4x³10x² + 7x-15 c. g(x) = 3x(x² - 4)5 d. y =…

A:

Q: Using Disk Method solution, R is bounded by x-axis, y-axis and the line 2x + 3y = 1. This is…

A:

Q: 9. Which of the following is equal to feedt? A. ee C. eºx + C B. ee + C D. eºt + C 10. What should…

A: As we know that; The Power rule: ∫xndx=xn+1n+1+C And ∫c·fxdx=c·∫fxdx , where c is constant   (9).…

Q: Evaluate S (2x - y) dx + (x + 3y) dy. C: arc on y = x5/2 from (0, 0) to (4, 32)

A:

Q: Find the area of the region enclosed by the inner loop of the limaçon r = 13 + 26 cos 0. [Hint: r ≤…

A:

Q: Find the indefinite integral. (Use C for the constant of integration.) 1₁ sin4 20 de

A: let  2θ=t⇒2dθ=dtThen∫sin42θdθ=∫sin4t dt2=12∫sin4t…

Q: Sketch the region whose area is given by the integral and evaluate it. Answer: 8 sin 0 Lote Lor r dr…

A:

Q: s x3 √1-x² V dx

A: Given: I=∫x31-x2dx   ...1   As we know that; The Power rule; ∫xndx=xn+1n+1+C

Q: 15 Find sin 2x, cos 2x, and tan 2x if tan x= and x terminates in quadrant III. 8 sin 2x = S ? cos 2x…

A:

Q: 4.) Consider the function defined as Find the following limits. a.) lim f(x) b.) lim f(x) c.) lim…

A:

Q: Solve the differential equation y' = 6x³y² subject to the condition that y = .1 when x = 1. y(x) = =…

A: We have to find the solution

Q: dx Find -given that dt 7x² + 6y² = 13 x = 1, y = - 1, and Give your answer as a simple fraction. dx…

A:

Q: The graph of g consists of two straight lines and a semicircle as shown in the figure. y 20 y = g(x)…

A:

Q: Estimate the integral 2de using a left-hand sum and a right-hand sum with n = 3 subdivisions.…

A:

Q: Rewrite the following series using the E-notation. 1 1 1 1 1 + + + + + + 10 17 26 37 12

A: Solving

Q: S dx x²-x+1 (x+1)3

A:

Q: Verify Green's Theorem by evaluating both integrals ƏN [ 1² dx + 2² dy - [ ] (™N - OM) a dA ax ду…

A:

Q: second derivative of y with respect to x from the parametric equations given 4) x=√1-t₁y = t³ - 3t…

A: We can find the required 2nd derivatives as below

Q: ∫ (1 + secx)2 dx Evaluate indefinite anti-differentiation

A: Solve it

Q: taylor series & radius of convergence of f(x)=sin(2x), centered at a= pi (22/7)

A:

Q: A plane flying horizontally at an altitude of 3.4 miles and at a speed of 790 mi/hr passes directly…

A:

Q: Use the midpoint rule with n = 6 to estimate the value of the integral (x³ + x)dx.

A: This question can be solved using the concept of mid point rule of definite integrals.

Q: A pendulum of length 10 cm has swung so is radian measure of the angle formed by the pendulum and a…

A: Follow the procedure given below.

Q: Consider the following. (1, 1) 2 6 10 X 4 X=8 -4 y = 2-x -6 -8F (a) Form the integral that…

A:

Q: 5. Evaluate [62³e¹dA; R= [0, 2] × [0, 2] R

A:

Q: Find f '(x), if f (x) = e−5x 5e O-5e^-5x 5e^-5x 5x

A:

Q: 1. Use a parametrization to express the area of the given surface as a double integral and then…

A: We have to find the surface area.

Q: 3. Find the area of the band cut from the paraboloid x² + y² -z = 0 by the planes z = 2 and z = 6.…

A:

Q: The supply function for a product is given by p = 50+ 100√2x + 5, where x is the number of units…

A: The supply function for a product is given by p=50+1002x+5, where x is the number of units supplied…

Q: Find a formula for the function f(x) such that f′(x)=tan⁡(x)x and f(5)=8. f(x)=  +∫   t= t=

A: This is a problem related to integration of the function. Derivative is given now by performing…

Q: Teddy got 87% in his Quarterly Assessment for Physical Education and Health. If there are 65…

A: Teddy got 87% in his Quarterly Assessment for Physical Education and Health. If there are 65…

Q: Identify and sketch the graph of the equation in R³. x = 1 − log₂ y

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

Q: √x x² ln x dx

A: