For each set of Polar coordinates (r, 0), match the equivalent Cartesian coordinates (z,y). Don't use a calculator. 1. (8, 7) 2. (8,5) 3. (-4,-3) 4. (8,4) 5. (11,-) 6. (-6,5) A. (-2,-2√3) B. (5.5, -5.5/3) c. (3√3,-3) D. (4√2,4√2) E. (-4√3,-4) F. (-4√2, 4√2)

Q: find dy/dx of each equation using implicit differentiation. a. y4 -2y2x2 + 3x2 = 0 b. (x + y)3 =…

A:

Q: y = (In x) x , find dy/dx. Oy y' = (In x)* (1 + ln x) O y' = (In x)*¹ [1 + x (ln x) (ln ln x)] O (E)…

A:

Q: 1. f(cos 3x - x²) (sin 3x- x³)5 dx 2. f cos² x (tan x) (sec² x − 1) dx 3. f tan x (sec² x - 1)(sec²…

A:

Q: Set up integrals for both orders of integration. Use the more convenient order to evaluate the…

A:

Q: At the end of each month, for 24 months, $200 is put into an account paying 9% annual interest…

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

Q: Find the derivatives of the following function (a) y=4²+2√²

A:

Q: dy √e²y-1 S

A:

Q: Given that the tangent and normal to a curve at point P(x, y) meet the x-axis in A and B…

A: It meets the x axis in A and B respectively and y axis in D and E respectively.To Find: Family of…

Q: Solve for 0 <0 < 2π Separate your answers with commas. 0= sin 40+ sin 50 = 0.

A: Here, the given equation is: sin 4θ+sin 5θ=0...(1)

Q: Find the volume of the solid generated when the region bounded by x = - sqrt(4y) . y = 4 and x= 0 is…

A:

Q: Decide whether the integral is improper. [ In(x²) dx proper O improper Explain your reasoning.…

A: Here we have to decide whether the given integral is improper.

Q: 3. (2 + y² + xy2) dx + (x²y + y + 2xy)dy = 0

A: As per the guidelines I can solve only one question

Q: Find curl(F x G) = V x (F x G). F(x, y, z) = i +5xj + 3yk G(x, y, z) = xi - yj + zk

A:

Q: 11. Given the function below, what is its derivative? * f(x) = 2x - √x f'(x) = 2x C f'(x) = 2 - a 1…

A:

Q: dx √1+√√x |

A: Given,  ∫dx1+x

Q: Verify that the hypotheses of the Mean-Value Theorem are satisfied for f(x) = √√x + 4 on the…

A:

Q: Find the divergence of the vector field F. F(x, y) = 4xe*i - 6x²y²j

A:

Q: Find a, and d for each arithmetic series. 61. $20=1090, 420= 102 63. S16-160, a16-25

A: Given that : S 16 = -160 and a16 . = -25.  is for a arithmetic series.   And we find the value of a1…

Q: csc(x) cot(x) 2-csc(x) a. b. In(2-csc(x)) + C O c. -2 In(2-csc(x)) + C O d. In(2-csc(x)) + C dx…

A:

Q: Find a Cartesian equation for the curve and identify it. ² cos(20) = 1

A:

Q: 8. For the enclosed regions bounded by y = x² - 6x and y = -2x in the graph, what is the integral…

A: Given   From the graph intersection point

Q: Determine whether the improper integral diverges or converges. 6° x²ex dx converges O diverges…

A:

Q: 4. Use mathematical induction to prove the truth of each of the following assertions for all n ≥ 1.…

A:

Q: b) Determine whether the series n=1 find its sum. Show All Your Work! n-l is convergent or…

A:

Q: 8. Sketch the curves and determine the area of the region formed in the given interval: y = √√2x, y…

A:

Q: 6. 22x+x dx

A:

Q: Show that if x is an integer, then gcd (x+1, x^2 -x +1) divides 3. Use this result to find knowing…

A: Solving

Q: 21 te 1 1 1-2 1-2 None of the alternatives are correct If L <=lim In p-400 then f(t) is 0+2

A:

Q: Using trigonometric substitution, Find the new limits of integration. (A) None of the choices B 2 6…

A:

Q: The f sin 2x cos 2x dx is 1+3 cos 4x 1 sin²4x + C 24 1 In|1 + 3 cos 4x| + C 12 {A} {B} {C} - In|1 +…

A:

Q: 11. f²(2x - 3) dx 12. ²₂(x³ + 2x) dx 13. f(x² – 2) dx

A:

Q: 2x²+x-1 Evaluate -dx using method of partial fractions. Which of the (x-1) (x³+1) following is the…

A:

Q: a₁ = 5 9₁2=35 Find the common difference using arithmetic sequence.

A:

Q: Consider a triangle ABC like the one below. Suppose that C= 123°, a= 15, and b=37. (The figure is…

A: The Cosine rule; a2=b2+c2-2bccosAb2=a2+c2-2accosBc2=b2+a2-2abcosC Given: C=123°, a=15, b=37

Q: Find the area of the region bound above by y = 2cosx and below by y = secx,-π/4 ≤ x ≤ 1/4.

A:

Q: Evaluate the following: 1) f sin x sin(cos x) dx

A: Integration

Q: 1. Find the derivatives of the following function (a) y=4²+2√² (b) y=++ 2x+3

A:

Q: Question 8 Find the derivative -[f (x)] dx Anmospace support = 3 In (In (x²-3x + 5)²) 3(2x - 3)…

A:

Q: a 10-foot ladder is leaning against a vertical wall when Jack begins pulling the foot of the ladder…

A:

Q: Find the derivatives of the following function (a) y=4²-3+2√ 2x+3 (b) y=2

A: We can answer the questions as below to find derivatives

Q: Set up integrals for both orders of integration. Use the more convenient order to evaluate the…

A:

Q: COS X 6. y = x What is the appropriate formula? dx Solution:

A: Given query is to find the derivative of the expression.

Q: 4. What is the SECOND derivative of the given function? * y = 3x³ - 2x² + x - √ y" =9x² - 4x + 1 y"…

A:

Q: Determine whether the improper integral diverges or converges. 00 x²ex dx 0 O converges O diverges…

A: Given query is to find integral converges or diverges.

Q: y = = Ax is YBC Ycs YBS = 1 -1 0 1 1 0 - D IB XC IS

A:

Q: 9x²-6 2x²-x²-8x+4 B D + x + 2 mx + n None of the choices 4 To evaluate A x-2 A 9 B 3 E 2 S + -dx…

A:

Q: Consider a triangle ABC like the one below. Suppose that b=58, c=34, and B= 108°. (The figure is not…

A:

Q: Find the 6th term in the binomial expansion below with Sigma notation. 8 3 3 / 4.x²³ - √x. - 3)

A: Let's find.

Q: 13-16 Sketch the region whose signed area is represented by the definite integral, and evaluate the…

A:

Q: How much money must be invested now at 10% interest compounded continuously so that $120, 000 will…

A: