Case 3: non-repeate quadratic factor (x²-x-21) Example 1: S 2x3-x2+8x-4

Q: The region bounded by f(x) = - 4x2 + 20x + 96, x = 0, and y = 0 is rotated about the y-axis. Find %3...

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Q: Given f(x,y) = e X cos y, Evaluate fx(0,2) cos 2 -sin 2

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Q: Graph the integrand and use known area formulas to evaluate the integral: dx

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Q: cos v f(x, у, 2) 3D xz2 af af 2 cos y Cosv siny df = - = - = - dx x2z2' dy dz xz3 XZ af cos v %3D af...

A: Topic:- partial derivatives

Q: Let F(x,y) = 2x + 3y . If (x , y) changes from ( 4,7) to ( 6 , 10) , find A F and dF. Enter AF in Bl...

A: To solve the following problem

Q: Find all the partial derivatives of: f(x, y) = y7 In(x²) + 9y¬3 – Vx*.

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Q: A post 20 meters long stands vertically in a horizontal plane. Another post stands vertically on the...

A: Given: A post 20 meters long stands vertically in a horizontal plane. Another post 45 meters high st...

Q: Use the Ratio Test to determine the convergence or divergence of the series. If the Ratio Test is in...

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Q: Question 8 A -tan(61) + C B 6tan( 61) + C B Ltan (61) + C D - tan

A: The given integral is sec2(6t).

Q: Question 4 x³dx (x²+2) ³ 1 A 2(x²+2) ' 2(x²+2) ? 1 1 В 2(x²+2) 2(x²+2) ² 1 +C 4(x²+2) ' 2(x²+ 2) 2 D...

A: Here, the given integral is: I=∫x3(x2+2)3dx⇒I=∫x2x(x2+2)3dx...(1)

Q: ind the general solution to the differential equation. dx dt = 3t2(x2 + 25) x =

A: topic- differential equations

Q: A bucket that has a mass of 10 kg when filled with sand needs to be lifted to the top of a 10 meter ...

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Q: 2) a. The graph ofthe function f(x) = ax²+ bx + c has the y- intercept of 3, and its tangent at the ...

A: Let's find. 

Q: Consider the function f : R → Rj, f(1) = (x – 4)°. Complete the following: fis because the equation ...

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Q: Find F'(x) if F(x)= e^(-x^2) * x^sin(x^3)  Use logarithmic differentiation

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Q: a. Find the open interval(s) on which the function is increasing and decreasing. b. Identify the fun...

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Q: Write the Taylor series for f(x) = sin(x) at x = as Cn x 2 n=0 Find the first five coefficients. Co=...

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Q: Calculus Business Application Worksheet 1. A manufacturer makes fuel tanks for cars. The total weekl...

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Q: Given f(x,y) = eX cos y, Evaluate fy(2,0) O cos 2 O sin 2

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Q: Find the indefinite integral. X COS 9TX

A: Given,I=∫ xcos9πx2dxPut u=9πx2Differentiatedu=9π(2x)dxdu=18πxdxdu18π=xdxThereforeI=∫xcos9πx2dxI=∫cos...

Q: Write the first five terms of the sequence with the given nth term. = cos %3D

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Q: Find the Maclaurin series and corresponding interval of convergence of the following function. 1 f(x...

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Q: The Maclaurin series of the function f(z) = 5z²e-# can be written as f(z) = E Cnz" where the first f...

A: Topic:- calculus

Q: Given f(x.y) = e X cos y, Evaluate fx(2,0) e2 cos 2 O sin 2

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Q: TRAN SFER TRANSFER ACTIVITY 2: INTEGRATION THROUGH SUBSTITUTION Direction: Evaluate the following in...

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Q: 2n a. Find the local extrema of the function f(x) = cos 3x + 3 sin 3x on the interval 0sxs and say w...

A: 0≤x≤2π30≤3x≤2πf(x) = cos 3x +3 sin 3xf'(x) = -3 sin 3x + 33 cos 3x f'(x) = 0-3 sin 3x + 33 cos 3x=0t...

Q: Find the indefinite integral: Sx(x³ + 1)dx x4 + x+c x/5 + x2/2 + c x5 + x2 + c O 5x5 + 2x2 + c

A: Find the indefinite integral

Q: Evaluate the integral by applying the following theorems and the power rule appropriately. Suppose t...

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Q: Use the Direct Comparison Test to determine the convergence or divergence of the series. 00 8n + n n...

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Q: Given the series 3" Σ n=1 antl find the ratio an (Express numbers in exact form. Use symbolic notati...

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Q: 1. Decide the limit: lim 2x + 3 X-3 2. Explanation 3. Can the function f(x) = 2x + 3 attain the limi...

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Q: Parametrize the following two curves in R3 and find their arclength. (1) the intersection of the cyl...

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Q: Evaluate the following integrals. Express the final answer in its simplest form and without negative...

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Q: Selecting 3 balls from a box containing 6 red balls and 4 blue balls. Combination Not Combination

A: We will find the given condition is a combination or not a combination in the following step.

Q: (A) Draw the graph of a function that has a secant line with m=3 between x=0 and x=2 , and a secant ...

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Q: find u*v where theta is the angle between u and v. llull=4, lvl=16, theta=2pi/3

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Q: A fourth degree polynomial with constant coefficients may have (1) 4 distinct real roots. (1I) 3 dis...

A: Topic:- polynomial

Q: Find the critical numbers of f(z) = 2? – 18z + 4 and classify all extreme values given 0 < z < 12. a...

A: In this question we have to find the values of Critical nos. and absolute value of max and min.

Q: 4. A rod is divided into ratio 1:3:5:6. If the 2nd to the shortest part is 35, find the length of th...

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Q: The functions represent the position of a particle traveling along a horizontal line, s(t) = 3t3 − 2...

A: for time t,t≥0 s(t)=3t3-20t2+48 t -20V(t) =dsdt =ddt(3t3-20t2+48 t -20)V(t) = 9 t2-40 t+48v(t)&gt;0 ...

Q: Find u•v, where tetha is the angle between u and v llull=4, llvll=16, tetha=2pi/3

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Q: 6. Calculate the area enclosed between the curve y =the curve y=x² and the line x= 1. Give your answ...

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Q: Find dyldt of y = sin (cost) and simplify. °v=- 1-t2 -t -Cos t Cos t y =

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Q: 10. Determine three positive numbers whose sum is 48 and such that their product is as large as poss...

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Q: Eight workers are assigned to 8 different jobs. Combination Not Combination

A: Eight workers are assigned to 8 different jobs. We have to determine whether it is combination or no...

Q: Write an equation for the function graphed below.

A: A graph is given in the question which is passing through point-10,0, -4,0, 0,10 and 6,0 andx=-3 and...

Q: Find dy/dx for: y = x2 − sec x + 1

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Q: Find ((dy)/(dx)) if y is a differentiable function of x and x^5+3y^4=x^5 tan y + 10

A: Given

Q: For each of the following matrices, either find its inverse or say how you know it isn't invertible....

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Q: A manufacturer has a steady annual demand for 10,850 cases of sugar. It costs $7 to store 1 case for...

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