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Q: is an angle in standard position, tan(e) 0, then the terminal side of lies in which quadrant? A IV…

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Q: Find the derivatives of the following functions: Inx i) y = sin3x? ii) y = e2*cosx iii) y = 3r+5

A: i)y= sin 3x2y' =ddx sin 3x2y' =cos 3x2  ddx(3x2)y'=cos 3x2 (3)(2x2-1)y'=(6x) cos 3x2

Q: Find f. (a) f'(x) = 3x4 – 5x? + x

A: Given query is to find the function.

Q: Verify Green's Theorem by evaluating both integrals aN dA Lv? dx + x² dy = ду ax for the given path.…

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Q: -2+0.5-0.125+...= (Write your final answer in fraction form, when applicable)

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Q: у" — у' — бу %3D2, у (0) %3D 0, y'(0) = 0

A: Given can be written as (D2-D-6)y=2 The general solution will be y=CF+PI Complementary Factor(CF):…

Q: de (x+2) h+2+ +C (r+2) x + 2- Option 1 Option 2 In Ix + 21 + 4r+5 + C in x + 2 (e+2) O Option 3…

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Q: Describe the graph of the equation. r = 15 sin 5t i + 15 cos 51 j O Itis a circle of radius 15 in…

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Q: xdy + (y – cos x)dx = 0, y (- = %3D

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Q: Find the unit vector in the direction of (3, -2). Write your answer in component form. Do not…

A: We will find the unit vector.

Q: x+1 dx

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Q: SHOW THAT THE DIFFERENTIAL EQUATION IS LINEAR EQUATION OF ORDER ONE 2. (y – 2)dx + (3x – y) dy =&

A: We can solve this problem as follows:

Q: Find the particular antiderivative of the following derivative that satisfies the given condition.…

A: I have stated the used formula in the solution

Q: sion into quadratic form, ax² + bx + c = 0, and ide %3D

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Q: Find the curvature and the radius of curvature at the stated point. r(t) = 7 cos(t)i + 3 sin(t)j+…

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Q: Find the moment of inertia with respect to x-axis of the area bounded by the parabola y = 4x and the…

A: Solution is given below:

Q: cos x e) f(x)= e* х

A: Topic = Derivative

Q: 14. Use the curve sketching procedure to analyze the function. a. y-x'+x²-20x а. 1+x? b. y=- 1-x?

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Q: 3 + In?x dx

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Q: (2xy+x^2+x^4)dx - (1+x^2)dy=0 the answer should be

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Q: 1 19 9. -10 -k Consider the matrix it corresponds to an augmented matrixial representation of a…

A: To find for given conditions of alpha and k and the system have how many solutions.

Q: Find V x (V × F) if F(x, y, z) = 8xyj+7xyz k. V × (V × F) =

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Q: If x + 1 f(x) then find the global maximum of on the interval [1, c0) Write DNE if there is no…

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Q: Find the derivative of the vector function r(t) = ta x (b+tc), where (5,-4, 1), b = {(-4, –3,1), and…

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Q: Find the general solution of the differential equation. dy = xy + 3x dx

A: To find the general solution of the following differential equation.dydx=xy+3x

Q: x2 dx (x+2)3 In |x + 2| + 4x+6 (*+2)a +C In |x + 2| – 4x+6 (x+2)a

A: To integrate.

Q: 5. Use the Second Fundamental Theorem of Calculus to find F'(x). х 1 F(x) = S* dt.

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Q: 4. a) Find the average value of the function over the given interval. f(x) [4, 25] Vx'

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Q: Write the given (total) area as an integral. a. The area above the x - axis and below y = 4 – x? b.…

A: area under the curve

Q: +y = e=* sin x

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Q: Find the constants a and b such that the function is continuous on the entire real line. x 5

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Q: Sketch a single graph of a function f which satisfies all of the following sign charts for f, f',…

A: We need to draw graph.

Q: 22. u = Vr² + s², r = y + x cos t, s=x + y sin t; ди ди ди əx’dy when x = 1, y = 2, t = 0 dt

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Q: Find the limits of integration ly, uy, Ix, ux, Iz, uz (some of which will involve variables æ, y, z)…

A: Given problem:-

Q: Show your work to determine the derivative of f(x) = (-1/x2 + 1/2 x2)(√x - 3x4). Do not simplify…

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Q: Find the area of the region bounded by the curves y = 1/x , y = x and y = 4x in the first quadrant.…

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Q: What is the result of multiplication of complex numbers -V3+i and (cos +i sin )?

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Q: Find the length of the curve r (t) = i + 6t°j + 2t°k, 0 <t < V1 L =

A: We will find the length of curve.

Q: dx 1-e-* Evaluate A. 2ln|e* – 1|+ c B. Inle* – 1|+x +c C. 2 In|e* – 1| +x+c D. Inle* – 1|+ c

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Q: What I Have Learned Let us now measure what you have learned in this module. Choose the letter of…

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Q: Determine the derivative of f(x) = 2x2 - x3 using the first principles definition of the derivative.…

A: Given f(x)=2x2-x3we know that using first principles f'(x)=limh→0f(x+h)-f(x)hThen…

Q: Find an arc length parametrization of r(t) = (e' sin t, e' cos t, le') r1(s) = (|

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Q: (6x- y+3)dx+(3y'-x-2)dy 6) Integration Factor Method rahee

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Q: Which of the following is undefined? cot() 131 A B sec(630") tan(-14n) D csc(-810")

A: Find which of the following is undefined.

Q: Use the first principles delta method to find the derivative of y = x2 – x. %3D

A: Here we have to find the derivative of y by using the first principles delta method.

Q: Consider the following statements. 1-If B is a symmetric matrix of 9x9 so the elements b32 and bz3…

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Q: x² + 4x + 1 dx (x – 1)(x + 1)(x + 3) d* - Inlx- 1+Inlx+11- n|r+ 3| +C Inlx- 11+Inlx+1| +Inx + 31 +C…

A: Let's find.

Q: H.W (5) Solve the following differential equations of (x'+y')dx+(2xy cos y)dy phee

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Q: Find the moment of inertia of the area bounded by the curve x^2=4y, the line y=1 and the y-axis on…

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Q: Find the distance between the two parallel planes 5x – 3y + z – 2 = 0 %3D -10x + 6y – 2z + 3 = 0

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