Use spherical coordinates to find the volume of a ball with radius R(in other words, use spherical coordinates to prove the volume formula V =4πR^3/3)

Q: if the limit at infinity exists find the limit lim(inf)=3x^3+5x/4x^4+10x^3+2

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Q: √9-x Consider the following double integral 1 = So So By reversing the order of integration of I, we…

A: Mark the limits on the graph and then reverse the order

Q: Use Part 1 of the Fundamental Theorem of Calculus to find the derivative of the function. S² (t =…

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Q: Determine if the Integral Test can be used for the given series. 1 in= √4n+1 a) The Integral Test…

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Q: 4 F(s) = 3s7 (s²+3)

A: First to find the partial fraction decomposition of the function: F(s)=43s7(s2+3) For that let,…

Q: Tutorial Exercise Find the absolute extrema of the function on the closed interval. y = 6 cos x,…

A: Given that, the function is y=6cosx. Differentiate the function with respect to x as follows.…

Q: 5. A. undefined B. 2 × 2 Consider (a) What is the size of QTP-¹? P= A. -1.5 B. -2 = [1 C. 2 × 4 D. 4…

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Q: Suppose that f(x) = 2x4 + 9x2. Evaluate each of the following: f'(1) = f'(-3) =

A: NOTE: Refresh your page if you can't see any equations. . take derivative

Q: 3x²+2 0 2x²+4x+3 Sort dx

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Q: Use synthetic division to find the result when 3x4 - 3x³ +16x²-117-31 is divided by a + 4. Write…

A: answer is in next step . please give a like !!

Q: It is a fact that the function  f(x) =  (9x2 − 2) (4x2 + 4)  has a limiting value. Use a table of…

A: We need to find limiting value.

Q: Find all cube roots of the complex number −1 + i

A: We have to find all the cube roots of the given complex number.

Q: 6. a) Determine whether each series is convergent or divergent. Carefully explain your reasoning.…

A: Given       ∑n=1∞1+3n1+4.3n                         let  an =1+3n1+4.3n…

Q: Find the exact sum of the following series O. In 3 2 1 In(3) --- / 2 In ( ²2 ) 32 3 In (²2) - ○…

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Q: Let F be the function below. If you are having a hard time seeing the picture clearly, click on the…

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Q: Use the definition for the function above to find the derivative. f'(x) = lim Submit Ax-o lim Ax-0…

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Q: Find the integral. J 3 x√9 - (In x)² + C dx

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Q: -4 -2 12- -8 -4 0 2 -N What is the equation of the graph shown here? 4

A: Let's find equation of given graph.

Q: (1) f(x+4)² dx (3) ſ. x² dx x² - 4 (2) √ x²(x³ + 1)² dx (4) √x²0 x² cos 3x dx

A: The given integrals are;  1) (x+4)2 2)x2(x3+7)7 3)x2/(x2-4). Repost the 4th question.

Q: I. Given: 3x - y - 2z = 1 -x + 6y -3z = 0 -2x-3y + 6z = 6

A: I am attaching image so that you understand each and every step.

Q: Tutorial Exercise Find the slope of the tangent line to the graph of the function at the given…

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Q: lim X→∞0 lim x118 √11+4x² 2 + 11x √11+ 4x² 2 + 11x = =

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Q: Let E be the solid region which lies above the region in the xy-plane bounded the curves y = √x and…

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Q: -4 Challenge #1 y = 2x 0 Adjust the equation so the exponential function passes through the points.

A: topic- exponential function

Q: Consider the following. x = 3 cosh(t), y = 2 sinh(t) (a) Eliminate the parameter to find a Cartesian…

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Q: • [√x S: z = 8x, 0≤x≤ 8, 0≤ y ≤7 Evaluate (x - 2y + z) ds.

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Q: Use Definition 7.1.1. DEFINITION 7.1.1 Laplace Transform Let f be a function defined for t > 0. Then…

A: Let f be a function for t≥0 then the integral Lf(t)=∫0∞e-stf(t) dtWe have to find the Lf(t)Where…

Q: For the following equations, enter y if the equation defines y as a function of x but not vice…

A: y if the equation defines y as a function of z but not vice versa, x if the equation defines z as a…

Q: For u(x, t) = f (x + ct) + g (x – ct), where c is a constant, find ux, ut, uxt . Show your work…

A: Given, u(x, t) = f (x + ct) + g (x – ct)

Q: Find the curl of the vector field F. F(x,y,z) = x sin(y) i - y cos(x)j + 5yz² k Part 1 of 3 It is…

A: The objective is to find curl F.

Q: 1) x(x + 1) dx S (3) x² x² +9 dx (2) √ x(x x(x + 1)³ dx (4) (x² + 1) cos x dx

A: Disclaimer:  “Since you have posted a question with multiple sub-parts, we will solve the first…

Q: Write the equation of the line shown. Be sure to use the correct variable. Equation:

A: NOTE: Refresh your page if you can't see any equations. . the given graph is as we can see the given…

Q: Consider the following. (Round your answers to four decimal places.) f(x, y) = x cos(y) (a) Find…

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Q: Find the complete solution of ey sin x dy cos²x = 0 dx

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Q: 1. Find the volume generated by revolving about x=1, the area bounded by y = (x²-₁)² and the x-axis.…

A: We have to find the volume generated by the given function.

Q: Find the distance between the point P(1, 1, 1) and the surface x² + 2y² + 3x² = 1.

A: Given Point P1, 1, 1 and surface x2+2y2+3z2=1

Q: curity According to a certain news poll, 63% agreed that it should be the government's…

A: Topic:- Probability

Q: The area of a square with sides of length s is given by A = s². Find the rate of change of the area…

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Q: 4. The height h in centimeters of Shuntaro's pogo stick from the ground as he jumps on it since s…

A: We have to find the height at given times.

Q: i) f si sin 3x cos 3x dx ii) [ cos³x dx

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Q: If the point (4,-7) is on the terminal side of the angle in standard position, sin (0) = cos(0) tan…

A: Here we have to find the value of trignometric functions.

Q: ow do you find the 70th derivative of f(x)=cos(x)

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Q: Find the curl of the vector field F. F(x, y, z) = arcsin yi + V1 - x2j + y2k

A: To find the curl of the given vector field F

Q: 8-2x ifx 4 (a) Find the limit of g(x) as x approaches the value "4" indicated below. To do this,…

A: answer is in next step . please give a like !!

Q: f(x) = 3x, a = 7

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Q: 2 i) [x² ( x + ²7 - 2²/1) dx x i) Ï 0 x³ - 8 x-2 dx ii) ii) f (x³ + 3x² + 1) e-2x dx xe xe1+x dx

A: Given:   i) ∫x3x+2x-1x2dx Expand   =∫x4+2x2-xdx Apply linearity     =∫x4dx+∫2x2dx-∫xdx

Q: Find the curl of the vector field F. F(x, y, z) = 4x² + 7y²j + 5x²k

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Q: (1) x² x² + 3 ſ dx

A: according to company rules,i have to solve one question when multiples questions are posted so…

Q: find the avg rate of change for the function over the given interval find the avg rate of change…

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Q: Our goal is to approximate the positive real number x that satisfies sin(x) = x³. We will apply…

A: Our goal is to approximate the positive real number x that satisfies sinx=x3We will apply Newton's…