find the exact length of the curve x = 2(e^t)cos(t) y = 2(e^t)sin(t) through 0

Q: Solve y'+9y=0, y(T) = −2, v′ (7) 6 y(t) = The behavior of the solutions are: 6 Oscillating with…

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Q: Express the integrand as a sum of partial fractions. x² 2 1 1 1 + -1 2(x²+1) 4(x+1) − 4(x − 1)…

A: Given query is to find the integral.

Q: Find the equation for (a) the tangent plane and (b) the normal line at the point Po(+1+116) on the…

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Q: Set up the definite integral that represents the area of ​​the region enclosed by the indicated…

A: Given equations of curve y = 2 - x2y = -x x = -2

Q: how do you justify part b?

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Q: Consider the following initial-value problem. 9x² - 12x, f(3) = 33 f'(x) = Integrate the function…

A: f'(x)=9x2-12xf(3)=33∫xndx=xn+1n+1+c

Q: 11. Find the equation of the tangent line to f(x) = 4x² - 5x+2 at (-1.11)

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Q: 35. y" - 2y"+y' = 2 - 24e* +40e³x, y(0) = 1, y'(0)=, y"(0) = −²

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Q: 27. x²y" + xy + y = 0, y(1) = 1, y'(1) = 2

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Q: Calculate the derivative of the following function. 5x y= 2x+7

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Q: Find an approximation of the area of the region R under the graph of the function f on the interval…

A: To find an approximation of the area of the region R under the graph of the function f on the…

Q: Use integration by parts to evaluate the integral: ∫ e^3x sin(11x) dx

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Q: an+1 n→∞ an Let (an)1 be a sequence with positive terms, such that lim [Hints: = = 2023. Show that…

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Q: Date Note Evaluate S √9-x² dx (use Trigonometric substitutions)

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Q: Determine whether the following function y = C₁x + c₂x³ + 2x² ex-2xe* is a solution to the…

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Q: Consider the following functions. f(x) = x² + 4 and g(x) = = Step 1 of 2: Find the formula for…

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Q: Let C(x) represent the cost of producing x items and p(x) be the sale price per item if x items are…

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Q: Determine the equation of a plane tangent to a given surface at a point. Find the equations of the…

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Q: Acceleration of a Car The distance s (in feet) covered by a car t seconds after starting is given by…

A: The given data is: s=-t3+14t2+18t, 0≤t≤6

Q: Given s(t)=4t+16t, find (a) v(t). (b) a(t). (c) the velocity and acceleration when t = 2. (a) v(t) =…

A: Given: s(t)=4t2+16t   Concept: The instantaneous velocity at a given time is the derivative of a…

Q: Let h(x) = X +² h'(x)= (a) Find the derivative using the Quotient Rule. = h'(x) = (b) Rewrite h(x)…

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Q: [2-R] [CLO 9] The set of solutions to the equation (x − 9)² + (y − 3)² = 49 is a circle in the…

A: Given query is to find radius and centre of the circle.

Q: For the function defined below, determine each of the following. f(x) = 5(x² - 12x +20) +20) ²/5 (a)…

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Q: Given the following functions: f(x) = cos(x) and g(x) = x¹0 + 1. Find: f(g(x)) = 9(f(x)) =

A: f(x)=cosxg(x)=x10+1d dx(xn)=nxn-1d dx(cosx)=-sinxd dx(constant)=0

Q: 41. y" + 4y = g(x), y(0) = 1, y'(0) = 2, 0≤x≤ π/2 x > TT/2 g(x) senx, 0,

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Q: II. For each function below find the critical points, the values at all critical points and…

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Q: Find the derivative of the function. f(x) =  2 cot x 1 + csc x

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Q: Consider the indefinite integral [3 Then the integrand has partial fractions decomposition a b cx +…

A: Given integral:- ∫5x3+7x2+36x+27x4+9x2dx

Q: Find an equation of the tangent line to the graph of the function f defined by the following…

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Q: b. Find and graph the velocity function. When is the object stationary, moving to the right, and…

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Q: Pls do fast and i will give like for sure Solution must be in typed form Which of the following…

A: we need to find out the instantaneous rate of change of function when x=3.

Q: A prime number is a number that is evenly divisible only by 1 and itself. 3. The prime numbers less…

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Q: Radioactive Decay Phospho after t days. (Round your growt

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Q: Find the limit by rewriting the fraction first. xy-2y-4x+8 X-2 lim (x,y) → (2.6) X#2 lim (x,y) →…

A: Given limit lim( x, y )→( 2 , 6 )xy - 2y - 4x + 8x - 2

Q: Find y' and y". y = cos(x²) y' -sin(x²).2x ✓ = y" =

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Q: Suppose f(x) = 19x + 18e. Find: f'(2) = =

A: To find f'(2)

Q: In Exercises 31-36, find the volumes of the solids generated by revolving the regions about the…

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Q: x²dx x² + 4 150. ·S₁

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Q: differential equation x-

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Q: Suppose f(x) = 19x + 18e. Find: ƒ'(2) =

A: Given: f(x)=19xe+18ex

Q: Sentwork Solve y'" - y" = e³x + 3e4x y = C₁ + C₂ x + C3e* + 18 e 3x + 16 4x

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Q: Let T be the triangle with vertices (a, r), (b, s), and (c, t) (and assume constant density). The…

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Q: Find the absolute extrema of the function. h(x) = ex² - 9 on [−3, 3] Absolute maximum value: at x =…

A: h(x)=ex2-9  on [-3,3]for critical point h'(x)=0d dx(ex)=exd dx(xn)=nxn-1

Q: Set up the definite integral that represents the area of ​​the region enclosed by the indicated…

A: To set up the integral which gives the area of region enclosed by given functions

Q: ) Sketch the graph showing the asymptotes and x, y-intercept points, Also find x²+3x-28 x-5 the…

A: Given function:- fx=x2+3x-28x-5

Q: Reduce the equation to the slope-intercept form: -5y + 7 = 0 5x + 3y = 0 x + y = 9

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Q: log, (log₂ (6x − 1)) = 2. -

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Q: The total cost (in dollars) of manufacturing x auto body frames is C(x) = 80,000+500x. (A) Find the…

A: Solution is given below:

Q: Integrate x²-x+6 x³ + 3x [² -dx. The partial fraction decomposition is (write all terms as…

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Q: 1 □ 10. If log; (x) = 17, what is the value of log₁/3(x)? 0 1 17 317 0-17 O 10¹7

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