30. x2/3 + y2/3 = 4, (-3√/3, 1) (astroid) УА О 8 x

Q: Find the exact length of the curve. = (1 + x²) ³/2, 18 3 20 3 10 3 y 0≤x≤2

A: To find length of the curve.

Q: 4. Given f(x) = (x² – 2x − 1)²/³, determine the equation of the tangent line at x=2.

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Q: A political scientist surveys 40 of the current 153 representatives in a state's legislature. What…

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Q: Two and one-half foot-pounds of work is required to compress a spring 3 inches from its natural…

A: Integration is used to find the work

Q: S* S* S*4cos(y) dydzdx 0 O 4r

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Q: Consider f(x)=x^4-2x^2+3 Note:Note: Use round parentheses for your intervals (open interval…

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Q: Find the geometric series or state that it diverges for n=0,infinity        e^-6n

A: We have to write  in geometric series and we have to give state for divergence

Q: Use implicit differentiation to find an equation of the tangent line to the curve at the given…

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Q: Use a graphing utility to graph the region bounded by the graphs of the equations. Then find the…

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Q: Find the local and absolute maximum and minimum values of f(x) f(x) = cos x, x ∈ [-3pi/2 , 3pi/2

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Q: Consider the following function. f(x) = 16-x2/3 Find f(-64) and f(64). f(-64) = f(64) = Find all…

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Q: Evaluate the integral. (Use C for the constant of integration.) | Vx2 +4 x²-81 dx

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Q: (³ a sin 3a da.

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Q: Evaluate √ √R 6xy5 dydx R where the region is bounded by the curves y = = x² 1 and y = 1-². Sketch…

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Q: 6. Use Calculus techniques and a calculator to solve this problem. Include explanation of how you…

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Q: Solve the following logarithmic equation. Be sure to reject any value of x that is not in the domain…

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Q: Calculate the slope of the tangent line to the curve f(x)=3/x^4.  When x =2

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Q: Complete the table shown to the right for the population growth model for a certain country. k=…

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Q: Find the amount of each payment to be made into a sinking fund which earns 8% compounded quarterly…

A: NOTE: Refresh your page if you can't see any equations. . the given future value is  FV=$34000…

Q: (a) y = f(x) A 0 16 32 48 (c) 16 16 F f(x) dx Enter an exact number. 40 (b) 0 F(x) dx 56 1.56 f(x)…

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Q: Express the integrand as a sum of partial fractions and evaluate the integral. x+2 √x72x -dx x²…

A: Given integral is ∫x+2x2+7x-8dx We need to solve the integral using partial fractions.

Q: 1. At all times, the length of the long leg of a right triangle is 3 times the length x of the short…

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Q: For each of the following rational functions, determine the horizontal asymptote for the rational…

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Q: Use partial fractions to find the indefinite integral. (Remember to use absolute values where…

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Q: 5 Given k (x) = 6x +x, answer the following: Part: 0 / 4 Part 1 of 4 (a) Find k(-x). *(-x) - y

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Q: Consider f(x)=x^3−3x^2−9x+4 Note:Note: Use round parentheses for your intervals (open interval…

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Q: 2. A catapult launches an object vertically upwards and after t seconds its height meters above its…

A: “Since you have posted multiple questions, we will solve the first question for you. To get the…

Q: Evaluate the given integral by changing to polar coordinates. JJ 5(x + y) dA where R is the region…

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Q: lve the exponential equation by expressing each side as a power of the same base and then equating…

A: Given query is to find the value of x.

Q: Solve the DE. (1 + y²) dx + (1+x²) dy = 0 O tan x + tan y = C e + ey = C O lnx + lny = In C arctan x…

A: Topic = Differential equation

Q: Consider the following cost function. a. Find the average cost and marginal cost functions. b.…

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Q: Find the area of the shaded region. 74 +3 sin(e) 0 414 D-1 41 2 32 2 41 2 EN

A: Topic = Area

Q: Change the Cartesian integral into an equivalent polar integral. Then evaluate the polar integral. 0…

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Q: Set up but do not evaluate an integral for the volume of the solid obtained by rotating the region…

A: Topic = Volume

Q: Consider the function h(x) = (x+1)f(x). Give the formula for the derivative h'(x). 1

A: Given query is to find the derivative.

Q: . A 24ft. ladder is leaning against a house while the base is pulled away at a constant rate of…

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Q: cos x x r² sin dr 1. f(x)= 2

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Q: f(x)=x+3e^x find (f^-1)' (3)

A: f(x)=x+3ex

Q: Solve the following exponential equation. Express the solution set in terms of natural logarithms or…

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Q: -3x+8 x-7 Fill in the blanks below. (Note that it is common to say a limit "has a value of" oo if…

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Q: 1. Complete the square to algebraically find the key features of the quadratic function. y=-3x² - 6x…

A: As per our guidelines we are only supposed to solve first three parts of questions

Q: Evaluate the limit using L'Hospital's rule if necessary lim (1 + 12) ² €-8

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Q: Solve the exponential equation by expressing each side as a power of the same base and then equating…

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Q: Evaluate the definite integral. Use a graphing utility to verify your result. 4 1₁2 x ²6² -2 x²(x³ +…

A: Concept: Applying integration rules ∫xndx=xn+1n+1+C

Q: Solve the logarithmic equation. Be sure to reject any value of x that is not in the domain of the…

A: Use logarithmic properties.

Q: Əw Find when r = 3 and s= - 3 if w = (x+y+z)²₁ x=r-s, y = cos (r + s), z = sin (r + s). ər Əw ər |r=…

A: We will find as shown below

Q: Determine whether the sequence with the given nth term is monotonic and whether it is bounded. Use a…

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Q: A car's rear windshield wiper rotates 105°. The total length of the wiper mechanism is 23 inches and…

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Q: Find the slope of the line passing through the points (3,5) and (3,-2). a) The slope is b) Select…

A: The line passes through the points (3,5)  and (3,-2)

Q: 51. 53. Soz z dz (a² + x²)³ dz LAVET A

A: