To evaluate x²cosx dx' use integration by parts. What is the expression after the second integration by parts? -2 / COST cosx dx + C cosx dx + C -2 / COST -2 / COST -2/sin cosx dx + C sinx dx + C x2sinx – 2x cosx+2 x2sinx – 2x cosx – 2 x2sinx + 2x cost – 2 x2sinx+2x cosx-2

Q: Calculate the average rate of change for the function f(x) over the interval-1≤x≤3

A: Topic = Algebra

Q: If f is continuous on [0, 1], prove that f₁¹ f(x) dx = f₁¹ ƒ(1 − x)dx.

A: This question can be solved using properties of definite integrals.

Q: 2 J xe9x da 0

A: Multiple questions-"As per our guidelines we are suppose to answer only one question.Kindly re-post…

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Q: Exercises To Solve [No.5] dx OS (x-1) √X²2X-3 dx 3-2x-x²

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A: We need to compare with general formula of backward difference.

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A: Given function, f(x)=-6x2+36x We know that function is said to be increasing when f'(x)>0, and…

Q: 1. u= x² + y² + z²

A: On solving this we will get

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A: We have to find the limit

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Q: y dy Vy+2 (√3+2-5) (5√3+2+7+21)+C (√3+2-5) (5√3+2-1+24) +C 3 Ⓒ(√3+2-5) (5√3+2+3y+24)+C…

A: I am going to solve the problem by using some simple calculus to get the required result of the…

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Q: Question 1 S x 1/2 dx and using the substitution = x 1/2, the resulting integral takes the form:…

A: The objective is to find the right option.

Q: Question 2 Determine the general solution. x (dy/dx) = 2 - 4x^3. O y=lnx-(1/3) x^2 + c Oy=2…

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Q: 4. Determine the number of terms in the sequence: -45, -32, -19, -6, 410 ***

A: There are 36 terms  in the sequence.

Q: 3. Find a vector equation of the line that... a) passes through (-3,5,-2) and (7,-3,1)

A: As per Bartleby answering guidelines if multiple questions are posted in a single picture then an…

Q: 2t Show that f/² sin tdt ≥ 7. (Hint: sin t ≥ ㅠ over [0, 1].)

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Q: Use Euler's method to solve the following ODES wwwwwwww dy dx = -2y + 4e¯*, with h = 0.18 from x = 0…

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Q: Find y dy S using the substitution +5=√√y+2 √y+2 (√3+2-5) (5√y+2+y+21) +C 3 (√x+2-5) (5√3+2-y+24) +…

A: I am going to solve the problem by using some simple calculus to get the required result of the…

Q: Use Cramer's rule to solve the systems in Problems 21-32. 21. 3x + 4y = 2 5x + 7y = 1 22. 5x + 8y =…

A: 22. The given equation is: 5x+8y=38x+13y=5 To use the Cramer's rule to solve the system of…

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Q: Arc length: Find the length of the space curve with vector equation r(t) =(4, 3cost, 3 sint ) over […

A: We have to find the arc length.   According to our guidelines we can do only one question so please…

Q: 5. Calculate the sum of the first 23 terms of the sequence defined below. tn 10+ 3n, n E N

A: We have to find the sum

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A: To find out the required value.

Q: need the answer quickl

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Q: Solve for the variable using a method of your choice. 72+7+72+6 7x+6= 8

A: The detailed solution is given below Thank you

Q: For the following exercises, find aj dt and direct substitution. 225. f(x, y) = ln(x + y), x=e¹, y =…

A: Given;  f(x,y)=ln(x+y), x=et, y=et.

Q: Compute[x² sin(2x)dx. A.- x² cos(2x)+ xsin(2x)+ cos(2x)+C 1 1 B. — — x² cos(2x)+ —…

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Q: 0 %16 0 رجوع > ۸:۲۹ م 4 من 4 sin x 6. f(x) = x2 + sin x ه الكاميرا ...| - = Find-f'(x)

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Q: Question 1. Let f(x,y) = y²e¹x. (a) Find the linearization L(x, y) of the function f at the point…

A: To find the linearization.

Q: 7. xdy = (5y + x + 1)dx Ans: y = -x-+cx5

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Q: Sketch the curve of f(x), a function whose first derivative has the following properties. You must…

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Q: Let u = 1-16x². For the integral with respect to u, one limit of integration will be 1. What is the…

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Q: Solve the differential equation using inspection method d'y d³y = 24. dx5 dx³

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Q: Find an equation of the line tangent to the graph of f(x) = (4x-3)(x+2) at (1,3). The equation of…

A: topic- equation of tangent line to the graph

Q: Pre Estimate the slope (slope = rise/run) of the tangent line to the curve. Q st 6 8 P 9 6 64 4 62 4…

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Q: The volume of a cube is growing at a rate of 225 ft3/min, and the length of a side is 5 ft. What is…

A: I am going to solve the problem by using some simple calculus to get the required result of the…

Q: Let f(x) = log2 (4x-x²)+2x. At what point is the tangent to the curve y = f(x) perpendicular to the…

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Q: Consider how we can evaluate this integral using u-substitution: x S dx. √2x+1 If we let u = 2x+1,…

A: This question can be solved by integration by substitution.

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A: a) Given that: xt=t2-t-6yt=4t3+3t2-6t For a horizontal tangent line, the slope must be 0. That…

Q: Curve Sketching y = x3 - 4x2 - 8x - 5 Show your work to determine: the y-intercept and any…

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Q: Evaluate √√√x² + y² ds along the curve r(t)=(4 cost)i + (4sint) j+3tk, -27 ≤t≤ 2T. C

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