f(x)=8x¹-7x³+2 on [−2,1]

Q: Find the area bounded by the parabolas (x-3)² - 16ky = 0 and y² - 16k (x-3) = 0.

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Q: 2x - 3 Examine the function f(x):= x²+4 from the point of view of monotonicity and give its local…

A: This question can be solved using the concept of monotonicity and local extrema.

Q: Consider vector v = (1,2,2), point A(2,5,4) and point B(-1,5,1) - In center-radius form, find an…

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Q: Calculate the volume of the solid of revolution generated by rotating the graph of the following…

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

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Q: ←…

A: Given

Q: Let r(t) = sin(t) and y(t) = 1- cos(t) All answers should be decimals 0.5 rounded to 2 decimal…

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Q: Find the area of the region bounded by the curves y=x4 andy=2x-x²

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Q: A bank has decided to set its interest rates to compound monthly on all deposits in order to give…

A: We know the compound interest formula:A=P1+rnntwhere A=Principal amount +interest Amount…

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: 1+coshxsinhx+(sinhx)2 It is true that cosh x = Select one: True False Using Increasing/Decreasing…

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Q: Using the method mentioned in Item #7, find the volume of the solid generated by 3 revolving the R…

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Q: x² + 4x + 1 (x − 1)(x + 1)(x + 3) dx

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Q: Show that the function f(x, y) = e2x cos(3y) satisfies the partial differential equation 4f + fyr =…

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Q: . Compute for the relation between the cubic inch and the cubic cm by taking the ratio of the volume

A: 1 inch = 2.54 cm    1 cubic inch  = (1 inch × 1 inch × 1 inch)  = (2.54 cm × 2.54 cm × 2.54 cm)  =…

Q: A bucket that has a mass of 25 kg when filled with sand needs to be lifted to the top of a 20 meter…

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Q: Find the area bounded by the parabolas (x - 2)² - 9py = 0 and y² = 9p(x - 2).

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Q: o - 23 dy

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Q: R(t) = (2 In|sec tl, sin 2t, cos 2t) Find the distance travelled by a particle along the curve…

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Q: f(x)-f(a) a. Use the definition mtan = lim x-a x-a b. Determine an equation of the tangent line at…

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Q: Find the volume generated by revolving the area bounded by x² + 4x + 4y + 8 = 0 and y=-2 about the…

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

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Q: Find the intercepts and the vertical asymptote of Enter the intercepts as points, (a, b). The…

A: To find the intercepts and the vertical asymptote of the following rational function.fx=x2-2x-3x-4

Q: 2 2 2 Find the moment of inertia: x3 + y3 = a3 about x = = 0.

A: Let's find moment of intertia.

Q: A ball is thrown upward from the top of an 800 foot tower. It's height above ground, h, t seconds…

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Q: S√4t² + 3 dt

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Q: 4. Find the limit, if it exists. If the limit does not exist, explain why. 3x²+4-4 (a) lim x2x²x2 2…

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Q: Find the coordinates of the centroid of the solid generated when the smaller region bounded by x² +…

A: We first graph x2+y2-6y=0 and y=6-x using a graphing calculator.  The shaded region will rotate…

Q: · ƒ³3(x + 1)(x + 2)²(x² −1)dx with and without the even-odd theorems (show both solutions).

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Q: The domain of the function f(x)=x+7/x-5 is all real numbers except x=5. Express the domain in…

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Q: A bucket is filled with sand so that the total mass (sand and bucket) is 15 kgs. The bucket is to be…

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Q: 2x fe²x sinx dx

A: Using integration by part.

Q: 205(1.31), where t is given in The population of a herd of deer is represented by the function A (t)…

A: Given,A(t)=205(1.31)t

Q: ds Find the complete solution of = 8t³√√s. dt

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Q: 3) Use L'Hopital's Rule to evaluate and check your answers numerically: 1 (b) lim x →0 sin² x 12/200…

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Q: Given: planes II₁ : 2x - 5y + z = −1 and II₂ : x + 5y + z = 5 intersecting on a line l (a) Compute…

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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: In the quadratic equation Ax²+BX+C =0 The roots are real and distinct. The roots are complex…

A: The given quadratic equation is Ax2+Bx+C=0

Q: vy B. Find the derivative of function f(x, y, z) = 3e* cosxy + ex² + Inzx at point P(1,0,) in the…

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Q: The circle of radius 1 centered at (-3, 4,1) and lying in a plane parallel to the yz-axis is a)…

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Q: 1. Consider the function f(x) = x6 - x³. a. Determine the absolute extremum using the First…

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Q: For what value of a, we have 0= . You may explain your answer below if you like (optional). (z) < 4

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Q: example of properties of definite integral

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Q: 2. Verify using the principle of Superposition that y₁ = ²* and y₂ = e* are solutions of y" - 7y'…

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Q: Find (a) v xw, (b) wxv, (c) vxv, and (d) wxw. v = i + 3j, w = 2i + 2j + 3k (a) v xw= (Type your…

A: Given query is to find indicated vector operation.

Q: Find the area bounded by the curves y-x² = -3,x+y = 3 and y = 0.5x.

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Q: 9. ydx - 4xdy = y'dy; y(4) = 1 Ans: -y²=

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Q: 0 W³ 6w² +3 dw

A: Given, ∫01w36w4+3dw

Q: 1. Consider the function f(x) = x6 - x³. a. Determine the absolute extremum using the First…

A: The given function, f(x)=x6-x3

Q: 2) Let f be continuous on [a, b], differentiable on (a, b) and positive (i.e., > 0) for all f'(c)…

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