1. Evaluate the integrals (a) fxsin 2xdx, (b) f(3x - 1) eª dx, Hint: Use the Integration by Parts. 3 (c) fx³ In xdx. X

Q: Evaluate the y' and Simplify the answers Inverse trigo functions y = √x² - 4 + 2arc(csc)

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Q: 1. Solve the differential equation (x-4y-3) dx-(x-6y-5) dy=0

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Q: Pls show complete solution (c) Set up the integral which yields the area of the indicated region R…

A: We need to setup integral for area.

Q: By method of Integration by Partial Fractions, A B(2x-2) + C (x³+5x²+6)dx (x²–2x+5)² = √ [₁²-2² +…

A: According to our guidelines we are supposed to answer only the first question if you want any…

Q: Find the height of a circular cylinder of max. volume that can be cut from a spherical wood of…

A: using double derivative test to find out height when cylinder volume would be maximum.

Q: Find the average value of the f(x) from z = 10 to z = 16 f(x)= √² - 100 I

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Q: Find the derivative of the following functions. Use long method. a. f(x) = 3x² + 5x - 100 b. f(x) =…

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Q: Evaluate the y' and Simplify the answers I Direct trigo functions y = x² sinx + 2xcosx - 2sinx

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Q: A product can be produced at a total cost of C'(x) = 500 + 100x2 + x³ dollars, where x is the number…

A: Given that; Cost function and revenue function.

Q: Solve (x + 1)(x + 2)²(x²-1)dx with and without the even-odd theorems (show both solutions).

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Q: Find the distance from the point P(1, 2, −1) to the line passing through the points A(−2, −3, −5)…

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Q: Ji 16 sin² x cos² x dx dx B

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Q: x-5 X-3+x-3' 31. Determine the lim A. 0 B. -00 C. +∞ D. does not exist

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Q: 7. Use Disk Method to find the volume of the solid generated by revolving the R bounded by y =√x =…

A: Given that Region bounded by y=1x+1,x=0,y=4Revolving about x axisUsing washer/disk mathod…

Q: Find the area of the region in the first quadrant bounded by the curve y = √x² +5, the x-axis and…

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Q: Please answer both

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Q: Find the derivative of f (w) = 7ln (w) + 18.

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Q: 1. A certain ellipse is centered at the origin from which the major axis is always equal to 25 and…

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Q: iven R'(t) = (4e²t, 2t ,2cosh t), and R(0) = (1, −2, 3), 1+t² find Ŕ(t), and give the parametric…

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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: Find the Area of the Surface obtained by rotating the curve about the x - axis y = cosh x, 0 ≤ x ≤ 1

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Q: Given: planes Π1 : 2x − 5y + z = −1 and Π2 : x + 5y + z = 5 intersecting on a line ℓ. (a) Compute…

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Q: Using Pappus Theorem, find the volume formed by revolving about the x-axis the area bounded in the…

A: We have to find the volume.

Q: u = xz siny + yz cosx + xy tanz

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Q: Consider the points K(-1,0, 7) and M(1, -2,5), the vector MN = (1,4, -3), and the line with…

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Q: Differentiate the function: y = e-x cos²x x²+x+1

A: To differentiate the function.

Q: Evaluate the double integral that will find the volume of a solid bounded by z = 4 − x^2 − 4y^2 and…

A: Let's find volume of solid.

Q: Use the method of cylindrical shells to find the volume generated by rotating the region bound by…

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Q: to determine the instantaneous rate of change c Use f(x+0.0001)-f(x) 0.0001 f(x) = 5x² - 7x ata = 2,…

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Q: _42. Evaluate: √(√√x - 2)dx 3 A. ++ C x 3 B. - + C x C. 3 +=+ C 2 D. -*²_³+C 2 x 12 Evaluato: ((2x…

A: Note:- Since you have asked multiple question As per our policy, we will solve the first question…

Q: c) 3,-1, -3, 3, -9, -27, ...

A: If the difference between two successive terms of a sequence is constant, then the sequence is…

Q: 10. Given the graph below, what is the value of x of the function H(x) is discontinuous? h(x)== A. 0…

A: Since you have asked multiple questions,  we will solve the first question for you. If you want any…

Q: Consider the position function s(t) = -4.9t +31t+24. Complete the following table with the…

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Q: Determine the Cartesian equation of the tangent line to C1 at the point where 0 = π/2. Given: polar…

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Q: Set up the double (dydx) and triple (dzdxdy) iterated integral that will solve the volume of the…

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Q: _ ²+2y — In(y + 1), find the arc length for 0 ≤ y ≤ 3 8 Given x =

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Q: Find the general solution to the differential equation dy/dx=x^2/y+3.

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Q: Enter a whole or decimal number, or DNE for does not exist or undefined. |0x| lim (5+10=¹). [ - -0+z

A: Topic = Limits

Q: Given the function f(x) = = Find the difference quotient Find f'(x) by determining lim f(x +h)-f(x)…

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Q: = Use the limit definition of the derivative to find the slope of the tangent line to the curve f(x)…

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Q: The volume of a cube is increasing at the rate of 4cm³/min. How fast is the surface area increasing…

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Q: Given x - ³²+2y — In(y + 1), find the arc length for 0 ≤ y ≤4 8

A: The arc length of the curve x=f(y) for a≤y≤b is given by ∫ab1+dxdy2 dy

Q: Integrate the following: 1. f xdx x²-x+1

A: The given integral is x/(x2-x+1). Repost the next question.

Q: Consider the function. x³ + 12 f(x) = X Determine the intervals on which f is increasing,…

A: A function f (x) is increasing on the interval I if f'(x) >0 for x in I. A function f (x) is…

Q: Find the inverse of 2=2-51.

A: Here, we need to find the inverse of z = 2-5i. So,…

Q: Use the limit definition of the derivative to find the instantaneous rate of change o ƒ(x) = 5x² +…

A: We have to find rate of change

Q: Find the area bounded by the parabolas (x - 1)² = 4ay and y² + 4a = 4ax.

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Q: Find the tangent plane (Xo, Yo, Zo) from f (x, y) = x² - 3y²; (0,1, -3)

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Q: For the following problems, find the general solution. 128. y" cos(x) + 2y + y

A: To find the general solution of the following differential equation.y''=cosx+2y'+y