3 x³e2x dx

Q: Consider the following curve. 1 + x 4 + ex Find y'(x). y'(x) = y = 1 Find an equation of the tangent…

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Q: Find the length of the loop of the given curve. x = 6t - 2t³, y = 6t²

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Q: Suppose c is inversely proportional to the square of d. If c = 8 when d = 2, find the constant of…

A: Function

Q: Does the series converge conditionally ot absolutely

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Q: dh ars of growth and shaping. The growth rate during those 4 years is approximated by d gs are 14…

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Q: Solve the equation dy 2y² – x² 3ry

A: GIVEN equation in this question dydx=(2y2-x2)(3xy)   SOLUTION- as we can see dydxis a homogeneous…

Q: Determine the exact value of the following expression. tan 137) 8

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Q: (x + 2y - 3)dx + (2x + 4y - 9)dy = 0

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Q: Consider the parametric equations below. x=3t-2, y = 2t+4 (a) Sketch the curve by using the…

A: We are required toa. graph the parametric equation x=3t-2,y=2t+4b. find the cartesian equation of…

Q: Solve the following recurrence relations: (a) an = 3an-1-2, ao = 0 (b) an 2an-1+(-1)", = ao = 2 (c)…

A: Since, you have posted question with subparts. As per guidelines, we are supposed to answer only…

Q: Find the quadratic function f(x) = ax² +bx+c that goes through (3,0) and has a local maximum at…

A: Given that a quadretic function f(x)=ax2+bx+c that goes thorugh (3,0) and has a local maximum at…

Q: Use Right-endpoint Rule with n = 5 to approximate ²x x√x+2dx to 4 decimal places.

A: INTRODUCTION:  The height of the approximating rectangle is calculated using the right endpoint of a…

Q: Consider the function f(x, t) = x³e-, where c is a constant. Find the indicated partial derivatives,…

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Q: (b) Given the graph of f (x) below (blue), select the correct graph of the transformation y = 2f (x)…

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Q: X √4- 4+3x² -dx

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Q: Find the length of the curve x = t³, 312 y = ²2² ²²₁ 0 ≤ t ≤ √3 t²,

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Q: Consider the following functions. f(x) = x², g(x)=√x-7 Find (fog)(x).

A: Given,            fx=x2 , gx=x-7

Q: Find the area of the following region. The region inside the inner loop of the limaçon r=5+10 cos 0…

A: Please see the below picture for detailed solution.

Q: 20. The widths (in meters) of a kidney-shaped swimming pool were measured at 2-meter intervals as…

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Q: The region between the curve y = √x, 0 ≤ x ≤ 4, and the x-axis is revolved about the x-axis to…

A: Given y = x0 ≤ x ≤ 4 as we know that volume pf solid bounded by revolution of y = f( x ) V =…

Q: 4- Say whether each given sequence is a geometric sequence, or not. Find the common ratio and the…

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Q: Find the area of the region bounded by the graphs of the equations. f(x)=sin(2x), g(x) = cos(x), -…

A: Please see the below picture for detailed solution.

Q: Twenty-three randomly selected students were asked the number of movies they watched the previous…

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Q: Find the particular solution of the D.E. y "+ 3y + 2y = 4e° = 4e* ON =e* 2 Oy₁ = / = Ae* + B

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Q: Express the following sum in sigma notation. Use 1 as the lower limit of summation and k for the…

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Q: 3) Find curl (xyi + yzj + zxk)

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Q: Find two points where the curve x² + 2xy + y² = 53 crosses the x-axis. The tangents to the curve at…

A: We need to determine slope.

Q: Use Stokes' Theorem to find the circulation of F = 4y? +7zj + 7xk around the boundary of the surface…

A: According to question,Given vector,F→ = 4yi→ + 7zj→ + 7xk→z = 64-x2 + y2for z≥0.

Q: Which of the following statements are true by the comparison test? A. The integral 5 da diverges…

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Q: 3. R is the region between f(x)=xln(x) and the x-axis on the interval [1, e]. (a) Write an integral…

A: Since you have posted multipart question i can do first three subparts as per our company guidelines…

Q: Find f(-1) + f(4), given the function: 14 11 04 13 x² + 1, if x 1

A: Topic = Functions

Q: (x) = x4−256x+4 Enter the x-values of any local minima, maxima, and inflection points.

A: Given f(x) = x4−256x+4

Q: Solve the system by back substitution. -4x-8y-2z - 6w = 5 -4y-24z-8w = -32 -4z-4w= -8 4w= 12 The…

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Q: $5,000 is invested for 5 years at 8% compounded quarterly, how much interest (in $) will be earned?…

A: Given query is to find the interest earned.

Q: 31. dy If x³ - 2xy + 2y³ = 4 then, in terms of x and y, dx

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Q: Find all points (x,y) on the graph of f(x) = 3x² - 4x with tangent lines parallel to the line y =…

A: Please see the below picture for detailed solution.

Q: Topic: Maxima-minima/optimization problems: Inverse trigonometric Functions For example, suppose we…

A: Minimum value= -pi/2  Maximum value = pi/2  For detail...go through the solution

Q: It's wrong

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Q: (c) At what points is the height 40 m? (Round your answers to two decimal places.) (x, y) = -52.825…

A: The given equation of the arch:y=211.49-20.96 cosh0.03291765x

Q: Differentiate the function. g(t) = 9t + 8t² g'(t) = 9+16x X

A: given  g(t)=9t+8t2we know  dtndt=ntn-1g'(t)=d(g(t))dt

Q: Find the area enclosed by the curve x = x = t² - 2t, y = √t and the y-axis.

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Q: A sailboat is sailing on a lake with a constant speed of 10 miles per hour. At noon, the sailboat is…

A: given  (1) speed of the sailboat = 10 miles/hr. (2) If at noon, t = 0, Then, at t = 0, the…

Q: Evaluate sin 5x cos 4x dx

A: NOTE: Refresh your page if you can't see any equations. . here we have

Q: for v= -1/2 cos (2x) where is -1/2 coming from? In the final answer, where does 1/4 come from?

A: Solution ⇒    Given function  ∫udv=∫x×sin⁡(2x)    here  u=xanddv=sin⁡(2x)…

Q: Sketch the region R and compute ff 2xdxdy, where R is the region bounded by x = y² and (x-1)² + y² =…

A: To find:- ∬R2xdxdy Where R is the region bounded by x=y2, x-12+y2=1

Q: 14. √9-x² x2 S dx

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Q: Use the Divergence Theorem to calculate the flux of F across S, where F = zi+yj + zxk and S is the…

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Q: : You need to provide a clear and detailed solution for the following Questions: Question 1 Given…

A: Solution: Given data, y"-7y'+10y = -2e3t

Q: (b) (i) Fill in the missing parts: The Ratio Test for (ii) Find the value of L. Σ gives L = lim n=0…

A: To use the ratio test

Q: Find F'(x) given F(x) = f ³² z S³ z³ dz. <-3x ○ F¹(x)= 54x³ ○ F'(x)=0 ○ F'(x)=81x³ ○ F'(x) = 162x³

A: fiven  F(x)=∫-3x3xz3dzwe know  ∫zndz=zn+1n+1+cdxndx=nxn-1