x³ + 3x dx. x2 + 1

Q: Solve the given differential equation. All solutions should be found. (8y" + 20°y) dx – (7xy° + x") ...

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Q: All edges of a cube are expanding at a rate of 6 centimeters per minute. Draw an accurate  picture t...

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Q: For the function (1- x if x 1 evaluate the limit lim f(x). メー1 (If a limit does not exist, enter Ø ...

A: This question is based on Limits calculation of a function.

Q: f(x) = -9.1688 × 10-6x³ + 2.7961 × 10-3x² – 2.8487 × 10-lx + 9.6778, Find the derivative at x=1.8 us...

A: f(x)= -9.1688×10-6 x3+2.7961×10-3 x2 - 2.8487×10-1 x +9.6778 X = 1.8 f(X) = f(1.8) = 9.174039892 h =...

Q: Newton's law of cooling states that the temperature of an object changes at a rate proportional to t...

A: Since u denotes the temperature of an object, dudt ∝ (u - ua)dudt = - k (u - ua)(Negative sign impli...

Q: Suppose y = V 2x + 1, where x and y are functions of t. (a) If dx/dt dy dt 15, find dy/dt when x = 4...

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Q: 33. tan- (z²y) = x + xy°

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Q: + 3x dz. x2 + 1

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Q: Evaluate the definite integral. 1 e? + 6 dz Jo ez + 6z

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Q: 12. Let F (x, y) : that = esin x+cosy (cos x,– sin y) and C = {(x, y): x² + y² 0. Show [ F- dR = 0 ...

A: Here we will use the Stroke's Theorem to prove the result.

Q: ax ve

A: To evaluate: I=∫dxex...(1)

Q: 2r da

A: Here we will find the integration, 

Q: Use the ratio test to determine whether the series converges. If the test is inconclusive, then say ...

A: Let's find. 

Q: Which of the following is the general solution to the differential equation 4xyº = -x² – y² for x> 0...

A: The differential equation is given as , 4xydydx=-x2-y2 find the general solution.

Q: -. Solve the differential equation: (D – 3) (D² + 3D + 2) = 0, where D is the differential operator ...

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Q: Find a differential equation that corresponds to the given direction field. Consider differential eq...

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Q: 8. Solve for all sides of the triangle. 12 40° 95 A

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Q: S cos²(2x)dx

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Q: Answer

A: Please refer to the image below

Q: Items 15 The graph of a function f is shown. On top of the graph of f, sketch the graph of f'. Use a...

A: The graph of the functions are given as 

Q: Find the inflection points of each of the given curve.  3y = x3 + 3x2 – 9x + 3

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Q: cos(2x) dx sinx+cosx

A: Given:         ∫cos2xsinx+cosxdx     We know that          cos2x=cos2x-sin2x        =∫cos2x-sin2xsin...

Q: Let f(x) = 5x + 20x². Then the equation of the tangent line to the graph of f(x) at the point (2, 90...

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Q: If f(x, y) = x cos y + ye", find dydx

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Q: sin –9xdx

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Q: a. As x approaches -1, f(x) approaches what value on the first table? On the second table? b. Do the...

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Q: Eliminate c, x'y =1+ cx (2+x3y)dx + xdy = 0 B (1+x?y)dx + x³dy = 0 © (1+x?y)dx + x²dy = 0 D (1+x3y)d...

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Q: Which of the following is not true? Of imit of f(x) as x approaches a is Land f(a)-L, then f(x) is c...

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Q: Consider the function f(r) - 6. 6x on the interval 4,5. Find the average or mean slope of the functi...

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Q: There is a jump discontinuity at x = 1 and lim f(x) = 1

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Q: 4. Figure 4.92 shows drug concentration curves for anhy- drous ampicillin for newborn babies and adu...

A: Basic calculus problem

Q: Find the derivative of y(x) = In (9(ln(x))’). (Use symbolic notation and fractions where needed.) dy...

A: To find the derivative of yx=ln9lnx7.  

Q: Use the ratio test to determine whether the series converges or diverges. If the test is inconclusiv...

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Q: Find the curvature of the motion of r(t) = . Leave your answer correct to two decimal places.

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Q: Answer the following True or False: Two cars drive from one spotlight to the next, leaving at the sa...

A: We can state the answer true or false with reason as below.

Q: 1.84 We call pa cluster point of E, provided that for all e > 0 there exists e e E such that 0 0 th...

A: We have to show E has no finite sub cover. 

Q: Evaluate the integral / cos (r) sin(x) dx 16 COS using the substitution u = cos(x). ,16 cos" (x) sin...

A: This question is based on indefinite integral.

Q: 6. Find the unit vector for which the directional derivative Duf(x,y) of f(x,y) = %3D 3x2 + 4y2 at t...

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Q: 1. Find the area of the region bounded by the graphs of the equation Y = x and y = x2.

A: Since you have asked multiple question, we will solve the first question for you as per our guide li...

Q: 1. x cot2 xdx X CO

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Q: Consider the following. cos(x) + Vy = 3 (a) Find y' by implicit differentiation. y' = (b) Solve the ...

A: Derivative

Q: For the given p-series, identify p and determine whether the series converges. -8/7 .Therefore the s...

A: The given series,       ∑k=1∞k-87

Q: Find an equation of the line passing through the pair of points. (-5) ( 1) 4

A: The equation of the line is solved below.

Q: If r(t) = , then unit tangent is a _______ , principal unit normal is a  ____ , and its curvature is...

A:   Given: r→(t) = ln t, ecos t, t2  

Q: Determine whether the alternating series converges. E(- 1*- k=3 7ln k k O The series diverges. O The...

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Q: 2. Explain how we know the function f(x)= 2.x is one-to one. Then find the inverse function f. x- 3

A: We are asked to  find the inverse of the function.

Q: Given the function: f(x, y) = 3x°y² – 72²y+ 5x – 4y Find the folowing: show complete solution fzy(x,...

A: Given:      fx,y=3x3y2-7x2y+5x-4y   a) fxyx,y:     fxyx,y=∂2∂y∂x=∂∂y∂∂x      fxx,y=∂∂x3x3y2-7x2y+5x-...

Q: » [3] S Te dx > Vex [4] S(x- s(x + !)° dx >

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Q: Postal regulations state that packages must have length plus girth of no more than 84inches. Find th...

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Q: The graph of y = f(x) has a y – intercept of 3 and the tangent line at the point (x, y) has an x- in...

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