Find the polar equation for the Cartesian curve ² Or 1 T= cos 2 1 Or=sin @tan 0 2 T = Or= Or T = 1 1 2 1 tan 0 2 sec 0 tan 0 -sin cos Ne 2

Q: Given x + y³ - 100y a.) Find all values of y that correspond to x = 7. Separate your answers by…

A: The equation is given by x+y3-100y=7                         ..........(1) To evaluate: (a) All…

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Q: Find the limit. lim (x,y) → (1,−4) 3x²y 2 1+xy²

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

Q: 4. I Find the general solution of the given system: dx1 dt dx2 dt = 7x1 +4x₂2 =-3x1-x2

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Q: 35. Choose the integral which represents the area between two curves given on the picture. 2- 1…

A: To choose the integral which represents the area between two curves given on the picture.

Q: Differentiate y = (2x³ + 3x² - 1)5 30x(x + 1)(2x³ + 3x² - 1) O 5(6x² + 6x)+ 30x(x+1)(2x³ + 3x² - 1)4…

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Q: Consider the function f(x) = Let F(x) be the antiderivative Then F(x)= - 8 2 x³ x6 - 4 of f(x) with…

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Q: Evaluate O O In 9 3 2 - In 2 In 2 x² 2 O tan¹ (2) tan¹(1) O ln 2 0 1 3 9 dx. x³ + 1 -

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Q: 2. Find from first principle the derivative with respect to x of the function f(x)= Inx.

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Q: Find the general solution of the given differential equation, and use it to determine how solutions…

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Q: Use the product rule to find the derivative of (4x⁹7x¹)(5e* - 4) Use e^x for e. You do not need to…

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Q: A license plate must contain 2 numerical digits followed by 2 letters. If the first digit cannot be…

A: Given 1. A license plate must contain 2 numerical digits followed by 2 letters. 2. the first digit…

Q: Test for convergence or divergence: e me emrin n=1

A: Find the limit as n tends to infinity

Q: S= 1 dx xinx

A: This is a problem related to integration. Please follow the procedure given below.

Q: Find the standard form of the equation of each ellipse satisfying the given conditions Foci:…

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Q: Find the slope of the tangent line to the curve 3 - 2x² + xy + y² I at the point (4, 1). - 27

A: This question is related to slope of line, we will solve it using given information.

Q: Find x² - y²¹ lim (x,y) →(a,a) x² - y² O 2a O 2a² a² 00 DO

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Q: Find the standard form of the equation of each ellipse. 9. 10. hori 16. 5 on test ор and ← 25 Find…

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Q: Find lim (√2-t, et-¹, In(t + 1)) t-0

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Q: Use linear approximation to estimate the amount of paint in cubic centimeters needed to apply a coat…

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Q: 5. Use the definition of a Maclaurin Series to express f(2) = as a Power Series. Give the 8th degree…

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Q: Suppose the demand for a product is given by D(p) = A) Calculate the elasticity of demand at a price…

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Q: At what time between 4 and 5 o'clock will the hands of the clock be opposite each other?

A: We have to solve given Questions.

Q: Match each of the following parametric Equations with a plane curve : x(t) = - 3t y(t) = 1 - 9t² TER…

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Q: Find the number(s) b such that the average value of on the interval [0, b] is equal to 6. f(x) = 6x²…

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Q: Consider the function f(x) = 2x³ 12x² 30x + 7 on the interval [-4, 7]. Find the average or mean…

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Q: Evaluate the interated integral: LS-² x² sin(y) dy dx

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Q: Use the Alternating Series Remainder Theorem to determine the smallest number of terms required to…

A: To use alternating series remainder theorem to determine the smallest number of terms required to…

Q: '() = xp (x-₂x) + xp (x + xx7)

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Q: If a ¤ R and 0 < x² < 1/2, which of the following expressions is equivalent to the geometric series…

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Q: Solve the following initial-value problems starting from yo 6. dy dt A. - 7y y = At what time does y…

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Q: f cos(x³) x² dx. O 1 ¹ cos4 + c 4 1 3 sin x²+ C 1 1 ¹ cos4 + c - 4 -3 si sin x³+ C

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Q: Q1) B- IF f(x)=√4-x, g(x)=x², Find : fog(x) draw them & determine (domain ,range). 9 gof(x),Then

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Q: Iƒ F(t) =î+tj+t²k and G(t) = tî+e¹+3k, then find (F × G)(t) at t = 0. 0 Ok O î+ ĵ + k o î+î

A: Topic- Cross Product of vectors

Q: For the function f(x) = 3x² −x³ – 4 where −3 ≤ x ≤ 3, complete the following. 1. Find f' and f". 2.…

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Q: 14. Evaluate f at its critical point(s). 15. Evaluate f at the endpoints of the given interval. 16.…

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Q: Use the definition of Taylor series to find the Taylor series, centered at c, for the function. f(x)…

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Q: Find the explicit solution of the initial value problem: dy dt 3 4ty+y y(1) = -5

A: We can find the solution as below.

Q: Find T(t) and N(t) at the given point. r(t) = 4 cos(t)i +4 sin(t)j; t = T T 3 N() = 73 π

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Q: ∞ f(x) = L n=1 (7-2x)" Sn

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Q: and f(a) f(x) = 4x² + 5x² + 6x-7 3 7 2. Find f(x), f"(0), given

A: Given a function f(x)=4x3+5x2+6x-7 We have to the following of the given function, f''(x) f''(0)…

Q: Let y = 5x² + 4x + 4. If Ax = 0.3 at x = 4, use linear approximation to estimate Ay Ay ~ Submit…

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Q: Find the average rate of change of the function over the given interval. f(t) = 2t² - 5, [3, 3.1]…

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Q: If y = f(x), f'(x), (f(x+h)-f(x)) and slope of the tangent to the curve of f(x), h lim h→0 they all…

A: if y = f(x) Then,  By first principle of derivative

Q: (1 + y²) dx + (x²y + y) dy = 0.

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Q: Consider the following vector function. 1, 12², 1²) (a) Find the unit tangent and unit normal…

A: The given vector function rt=3t, 12t2, t2

Q: Find the general solution to the differential equation: y' = 8x + e²r

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Q: Funktionen f(x) har följande graf: -3 -2 w 1 101 5- -10- Vilken, eller vilka av funktionerna nedan,…

A: Disclaimer: since you have asked multiple sub parts of a question, we will solve only first three…

Q: 23. The distance from a point (2, y) to the line 4x + 3y =0 is equal to 5. Find the value of y. O…

A: Given that the distance from a point 2,y to the line 4x+3y=0 isequal to 5. We need to find the value…

Q: Use substitution method to evaluate the definite integral fore dx

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