1. Evaluate the integral f 2³+6²+12r+dr. (Hint. You may need to use partial fractions and trigono- (x²+4x+5)2 metric substitution techniques to evaluate this integral).

Q: r(t) = (0,8 cos³ 10t, 8 sin³10t), ≤ t ≤ 4

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

Q: 3. sin² 3xdx

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Q: Question 2 Let f(x, y) = 5e¹* sin(3y) af д х af dy =

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

A: See this solution in below.

Q: Find the area of the region bounded by the curves y = xe -0.4x Area = x = 5, and y = 0. >

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Q: dy 9. Given the curve xy - y³ = 7, find dx y [A] xyz [B] 3y x-y² y [C] -²/3 [D]x-3y [E] y x-3y²

A: On solving this we will get

Q: Find and classify (as a relative maximum, etc) all critical points of j(x, y) = 2x³ + 3xy + 2y³.

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Q: Suppose that the plane tangent to the surface z=f(x, y) at (−1, 4, 5) has equation z+5x+1y=4…

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Q: Question 9 Determine the derivative of the given function: y = ²2t Oy=t² (2¹) + 2(2¹) (t) Oy In 2(2)…

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Q: The corners of a rectangular plate have coordinates (2,2), (8,2), (8,8) and (2,8). The density of…

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Q: Given the following differential equation: (y³+ kxy4 - 2x)dx + (3xy² + 20x² y³ - ky)dy = 0 a) Solve…

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Q: S x² x²+49 -dx

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Q: Find the differential dy of the given function. (Use "dx" for dx.) y=x√√√9-x² dy ||

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Q: What else do you observe? Concept Check: Evaluate the following integrals: e3x dx 1-2e3x 2.5 1²…

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Q: If a and h are real numbers, find the following values for the given function. The function is…

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Q: Find the interval(s) on which ƒ(x) = |x² − 5x + 15 is differentiable. Enter your answer using…

A: The given function fx=x2-5x+15 We have to find the interval on which fx is differentiable.

Q: If f(x) = 2x² - 3x + 6, find f'(5). Use this to find the equation of the tangent line to the…

A: NOTE: Refresh your page if you can't see any equations. . take derivative

Q: 3. fxe (4-x²) dx

A: ∫ xe4-x2dx

Q: Suppose that the graph of the velocity function of a particle is as shown in the figure, where t is…

A: Remember that: Time t is taken on x axis and velocity is taken on y axis. The particle moves forward…

Q: 25. If a and h are real numbers, find the following values for the given function. The function is…

A: The numbers a and h are real numbers. The function is f(x)=x2-x+1

Q: Problem 2 Given the following differential equation: (y³+ kxy4 - 2x)dx + (3xy² + 20x²y³ - ky)dy = 0…

A: Concept: Take into account the equation P(x, y)dx + Q(x, y)dy = 0 . If v(x, y) = c, the differential…

Q: Finally, determine (x³. - x + 8) and simplify the result. Recall that multiplication is commutative…

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Q: Which of the following is true about a differentiable function f(x) whose inverse is g(x). og (2) =…

A: To find the derivative of inverse function.

Q: Let r(t)= (212-t,t³ +1²-5t), -2≤t≤ 2. (a) Sketch the curve which is generated by r(t). You may use…

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Q: Obtain the differential equation of this family of curves. The lemniscate ² = acos 20

A: see below the answer and calculation

Q: 1. Find a particular solution to y" + 4y + 4y= 25 cos(t). Solution yp(t) =

A: As per guideline we can solve maximum one question you can repost other question

Q: f(x) = z3 + 6 +6 3-4x-2

A: If y=u/v  then y'= (v×u'-u×v')/v2

Q: Question 8 A graph displaying the relationship between the value of a stock and time is shown below.…

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Q: A farmer has 100 feet of fence with which he plans to enclose a rectangular pen along one side of…

A: Given query is to find the dimenyfor maximum area.

Q: 6) F(x) - (23x44) (x2 Sinx + 3x) + 3x)

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Q: Find the second derivative of the function f(t)= t³sect. Of"(t)= t³sect(20+tsect+10ttant+ftan²t)…

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Q: Fill in the first 3 levels of Richardson extrapolation to estimate the derivative of sin(x) at x =…

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Q: ƒ(x) = 5 4x³+4

A: To differentiate the given function using quotient rule.

Q: Find the area of the region bounded by the y-axis, the line x=3, and the functions f(x) = (x² - 3x +…

A: We have to find the area of the region bounded by the y-axis, the line x=3, and the functions…

Q: ✓5. 4y³(x² +4) dx + 4xy¹ = (x² +4)² dx

A: Given differential equation:- 4y3x2+4dydx+4xy4=x2+42

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Q: (a) f(x) = 2x³ - 3x²-12x+1 on [-2,3]

A: As per our guidelines we are allowed to solve only one complete question. Kindly repost others.…

Q: Consider the following functions: f(x) = 16-3x - x² 22 g(x) = 5-2x Evaluate (fog)(x). O-4x² +26x -…

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Q: 2. In a. and b. (below), show that y₁() satisfies the given differential equation. Then, use the…

A: Given data:- The given differential equations, (a); 2t2y''+ty'-3y=0,       y1t=t-1 (b);  4x2y''+y=0,…

Q: Given: y = 5 (cosh log )², find y' (cosh² O g = =|sinh 2 log = ]5 sh®log }} O 5 O ý =−}(m& )[sinh 2…

A: The objective of the question is determine the derivative of the given function and choose the…

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Q: The volume of a cube with sides of length s is given by V = s³. Find the rate of change of the…

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Q: Application of Derivatives (Tangent Line, Normal Line, Rate of Change)

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Q: How do you get the exponent of 1.67?

A: Given solution :

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Q: Find the derivative, y', of the function y = sinh(lnx) - cosh(lnx) O y = 0 O y = 1 Oy = 2/ 0 y =…

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Q: If √x + √y = 12 and y(1) = 121, find y'(1) by implicit differentiation. 11- X

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Q: Find the following using the table below. I f(x) 1 2 3 4 3 2 4 1 1 3 1 2 3 1 4 f'(x) 2 4 g(x) 4 3…

A: Given thatthe table To find :1. h'2 if hx=fx.gx2. h'2 if hx=fxgxSolution…

Q: dv 22² = 3/ dt v-1 32 a) Write the given first-order LDE in standard form. b) Solve for the general…

A: Since you have asked a question with multiple parts in a single request we would be answering only…