Convert the rectangular equation to a polar equation that expresses r in terms of 0. ²=5y (Type an expression in terms of 0.) .....

Q: Find f(x) such that • ff(x) dx = 1/√ √ x² + 4 + C

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Q: S By an appropriate trigonometric substitution, S: I 1 √10 sin 0 cos² Ode Cos 0 10 sin 0 -do |…

A: Here we will use Trignometric sunstitution for given integral.

Q: 14. 2y dx + x(x² In y − 1) dy = 0. -

A: To find the solution of the given differential equation.

Q: For the function y = f(x) = 3x³ – 10: df dx a. Find ƒ'( − 2) b. Find a formula for x = f-1(y).…

A: NOTE- "Since you have asked multiple question, we will solve the first question for you. If youwant…

Q: Find the curvature (t) of the curve r(t) = (−4 sin t) i + (−4 sin t)j + (1 cost) k

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Q: Use summation properties and formulas to rewrite and evaluate the sum. 31 Σ [(3i)² – 6i] - i=1

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Q: X 2000 A television camera at ground level is 2000 feet away from the launching pad of a space…

A: A television camera at ground level is 2000 feet away from the launching pad of a space rocket is…

Q: 3 Compute the rotated area bounded by x = y, x = 8 and x-axis about y-axis

A: Please note that as mentioned only the last question is solved.

Q: S 3 T 2 For the above rational function f(x)= 3 Q 17 2x² +2.5 . identify the interval on which f is…

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Q: 3) Evaluate xả 5x+1 dx

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Q: (a) √3x³ + 3x - 2 dx (b) √3x²+√x dx √x (c) főz (z ² − z− ¹) dz (d) 2² (3−u)(3u + 1) du

A: Since, you have posted multiple questions, as per guidelines we will solve only first question. If…

Q: Find the equation of y, given the derivative and the indicated point on the curve. dy dx = 2x - 1 y…

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Q: Find the solution to satisfying _y(t) = dy dt = 2y y(6) = 9

A: The given differential equation is; dydt=2y As we know from the integral rule,  ∫1ax+bdx=1alnax+b+C

Q: Find the indefinite integral. (Remember to use absolute values where appropriate. Use C for the…

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Q: Find a function y(x) such that 6yy' = x and y(6) = 3. y =

A: The objective of the question is solving the differential equation.

Q: Use the alternative form of the derivative to find the derivative at x = c (if it exists). (If the…

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Q: A particle moves along the x-axis so that its position at time 0 ≤ t ≤ 18 is given by x(t), whose…

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Q: Use the appropriate limit laws and theorems to determine the limit of the sequence. 92n an = n! (Use…

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Q: 5. dy/dx = sin(x + y). ANS. x+c = tan (x + y). sec (x + y).

A: Please see the below picture for detailed solution.

Q: Five years after purchase the auditor of a newspaper company estimates the value of their printing…

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Q: Evaluate functio J dx x² - 6x + 13

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Q: -10 -5 у 10- 5 -5 -10- 5 E . 10 X

A: We need to write down the type of the function, x and y intercepts and also the vertical and…

Q: Use interval notation to determine where f(x)>6. 2. Use interval notation to determine where f(x)

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Q: ve passes through the point (0, 9) and has the property that the slope of the curve at every point P…

A: Topic:- application of integration

Q: Find the derivative of x 1 f(x) = = 1₁² 1₁ ²² 16 dt S 1+t6 4 f'(x) =

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Q: 1. Express the following equation in vertex form: y coordinates of the vertex point. 2 = 3x² 12x +…

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Q: Consider the region R bounded by the functions f(x) 3x and g(x) = x² + 2. The ar a. 2 sq. units b. 3…

A: Topic:- application of integration

Q: (b) Find a particular solution for each of the given differential equations (i) y" - 6y +9y = e² - 5…

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Q: ΣΠ n=1 a. 1+4+1 6n 61 5 b. 41 5 is equal to c. The series diverges. d. 66 5

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Q: Procedures and Problem Solving Finding the Domain and Range of a Function In Exercises 7-10, use the…

A: Given: Graph is given

Q: Find the extrelne values of the function f(x,y)=4x2+ 7y2, on the circle x² + y²=1.

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Q: Express the polar coordinates 5, 11t 6 in Cartesian coordinates. What is the point in rectangular…

A: Given: Polar coordinates 5,-11π6

Q: _____18) Find y' if y= 6+x √4-x²

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Q: 10. Which of the following is FALSE about the parabola for the function f(x) = (x + 2)² − 6 a) The…

A: The given parabola function fx=23x+22-6 The general parabola equation y=ax-h2+k where, h,k be the…

Q: Need

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Q: 2. What is the maximum value of the parabola shown? y = - 2(2x − 1)² - 5 a) x = -1/ b) y = -5 c) x =…

A: NOTE: Refresh your page if you can't see any equations. . the given equation is  factor out 2

Q: 2y dx + x(x² In y − 1) dy = 0.

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Q: Use the Ratio Test to determine whether the series converges absolutely or diverges. 8 Σ k=1 3k² 7k…

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Q: (2x² + 2xy + y²) dx + (x² + 2xy - y²) dy = 0

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Q: (1+x²)y' + 2xy = (1+x²)y

A: Given problem:- 1+x2y'+2xy=11+x2y

Q: y² = -25x 10- + the equation of the me focus is (Type an ordered pair. Type an integer or a…

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Q: 2. Simplify the radical expression: 7 2 -1 156x y z -5 -1 2 √39x y Z

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Q: Evaluate the piecewise function at the given valuesof the independent variable. f(x) = { 5x+3 if x<…

A: Given piecewise function is  f(x) = { 5x+3 if x&lt; 0            { 4x+7 if x ≥ 0 We have to find…

Q: Compute the rotated area bounded by y = 2x, x = 2 and x-axis about x-axis

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Q: Given an, if limn→∞o an = 0 then the series 1 ∞ O diverges O converges O inconclusive O None of the…

A: series

Q: Given the curve shown below, determine if the slope of the curve at x = negative, or zero. 4 3 2 O…

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Q: J 1 cot³ x O 3 2 dx = In | sec² x − 1| + C --- O 1 tan² x + ln | sec x + C 4 O 1 2 O 1 2 1…

A: I have stated the used formulas in the solution

Q: If the substitution y = x is made, the integral - 1 64 2 3x³ 3+x² 3x³ 3 + x² .64 18x8 3 + x² S™ [²3…

A: The objective of the question is rewrite the integral  and choose the correct option.

Q: A manufacturer has determined that the total cost C of operating a factory is C = 2x² + 60x + 200,…

A: Firstly we have to solve for average cost per unit as given in the question.  Then apply…

Q: Find the area of the surface. The part of the plane 3x+2y+z=6 that lies inside the cylinder x² + y²…

A: Since, the equation of the cylinder is x2+y2=4 and  3x+2y+z=6⇒z=6-3x-2yParameterize the surface of…