1- x2 If f(x) = then f'(x) = x² + 1 2/x(x² + 1)³

Q: Given: z = a' + æy", r = uv² + w®, y = u + ve" az Find when u = 2, v = – 3, w = 0 dv

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Q: The graph of the function f (2) = 2 arcsin(x – 4) +1, is best pictured by:

A: We will put the x values and get the f(x) values.

Q: Find the exact value of the expression, if possible. (If not possible, enter IMPOSSIBLE.) arcos…

A: Givencos-1cos-3π2We know…

Q: 10 dx 5. S (10 +1)5 6. S 2r(e**+1 – 2**) dx

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Q: 5. Evaluate the integral Vxdi +C 2/3 +C 1 +C 3x213 O None of these

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Q: Find the volume of the solid obtained by rotating the region bounded by the given curves about the…

A: Given:-the region bounded by x=y4,  x=1rotating about the line x=7using washer/disk…

Q: Which is the power series representation (a) n! n=0 (b) -1)". (2n)! n=0 2n+1 (c) X-1)* (2n + 1)! n=0…

A: We have t

Q: Q5) Find the integration by using (by part method): S e3X sin X dX

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Q: For what values of a and b is the line-5x +y b tangent to the curve y = ax when x = 37 a = b D %3D…

A: -5x +y  =b    and curve is y = ax3 at x =3 here for tangent the slope of curve and line is same…

Q: Consider the differential equation xy" + 3xy' - 3y = 3x - 2x. (a) Verify that yi = x and y2 = x…

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Q: Find the Maclaurin series for the given function f(x) = e-6x

A: The maclaurin series is: f(x)=e-6x     ,    f(0)=1f'(x)=-6e-6x     ,    f'(0)=-6(1)=-6f''(x)=36e-6x…

Q: Answer the question in FULL details. Show ALL your steps and work in your calculations. Answer in…

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Q: Find the sum by adding each term together. Use the summatlon capabilitles of a graphing utility to…

A: we have to find sum.

Q: dz Find given: dt z = ze", z = t°, y = 1+ 4t dz dt Your answer should only involve the variable t

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Q: Use the fourth Taylor polynomial for f(x) = Va at a = 9 to estimate v10. Round your answer to four…

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Q: t*dt then If f(x) = 3 f'(x) =

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Q: Find the indefinite integral. (Use c for the constant of integration.) (4t³i + 10tj – 3Vtk) dt

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Q: Condense the expression to the logarithm of a single quantity. log (x + 1) + 2 log3(x - 1)] + 6 log3…

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Q: Find all points (if any) of vertical tangency for the curve represented by x = t? + 2t – 3 and y =…

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Q: Which of the following systems of linear equations has a solution of (-2,-8)? S 8x + 2y = –32 | y =…

A: To determine which of the following systems of linear equations has asolution of -2, -8.1…

Q: ||r'(t) x r"(t)|| Use the formula k(t) to find k(t). 13 ||M(t)||* 15: r(t) = t’i + tl5j K(t) =

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Q: Use the finite difference method to solve the system of equation given by: y'"' + 2y" + y' + y = x²…

A: Given :y'''+2y''+y'+y=x2                                   (i)y(0)=0.2, y(1)=0.8 & y(2)=0.2We…

Q: QI: Find dyldx for the following functions:- (3) y = (tan x)tnz+ t (4) y = sin-(x² +x) + 5"

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Q: 49 x dx -7

A: answer is in next step

Q: valuate the integral by interpreting it in terms of areas. In other words, draw a picture of the…

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Q: a) Determine the position function, s(t), of an object if the acceleration is a(t) = 5t , (3) = 0,…

A: We know that a= dvdt, v= dsdt In particular, when velocity is positive on an interval, we can find…

Q: 1. 3 de

A: Given integral,         ∫3 dx

Q: 2. A rocket is launched in the air. Its height (in meters above sea level) as a function of time t…

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Q: 5. What is the general solution of the following differential equation ( .6³yod?y =0)? ,d*y +9. dx2…

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Q: 1. Calculate the following limits (showing all working): log,(n) + 5" n-0o log7(n) + 7" Vn5 + 2 +…

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Q: Find the Indefinite Integral and check your result by differentiation. (Use C for the constant of…

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Q: Find the tangent plane to the equation z 5z° + 4y – y at the point (4, 2, – 66)

A: Given: z=-5x2+4y2-y      4,2,-66

Q: Evaluate the definite Integral by the limit definition. Step 1 To find the definite Integral dx by…

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Q: Use the chain rule to find and , where as z = x² + xy + y, x = 6s + 9t, y = 5s + 8t %D First the…

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Q: 92. tan? do 3

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Q: Q2 Evauate : fx V+1 dx

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Q: Evaluate csc2 3z dr cot 3r O 6cot 3xcsc3x + c O cot 3x + c Ocot 23xcsc3a + c cot 23x +c

A: Indefinite integration

Q: In each case determine if the Diophantine Equation has a solution. If it does find two solutions.…

A: Euclidean algorithm: Note that the greatest integer that divides both A and B is the Greatest Common…

Q: Find the series radius and interval of convergence for what values of x does the series converge x"…

A: We need to find radius and interval of convergence.

Q: Solve the exponential equation algebraically. Approximate the result to three decimal places. (Enter…

A: We have to calculate value of x.

Q: 7. Given that tan (A) = - and angle A is in 3rd quadrant and cos(B) = - and 13 angle B is in 2th…

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Q: Given z = f(а, у), а — г(и, v), у — у(и, v), with 2(0, 2) = 1 and y(0,2) 4, calculate z,u(0, 2) in…

A: We have to find the value of zu(0,2).

Q: Find 8 i8 Z = -12 ti2

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Q: dx 5-x?

A: We will solve the integral.

Q: lim TDC – 1 2x?

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Q: (8x + 4x)v4x² + 8 – 24x³ – 32x If f(x) = (/4x2 + 8 - x*) then f'(x) = 4r2 +8

A: f(x) = (4x2 +8 - x2 )2 f'(x) = (24x2 +8 - 2x2)(8x/(24x2 +8)  -2x ) f'(x) = ((24x2 +8 - 2x2)(4x -…

Q: Find the volume of the solid Formed by revolving the region bounded by the graphs OF y=x +1, y = 0,…

A: Find your answer below

Q: Find the volume between the cone y = Vx² + z² and the sphere x2 + y² + z² = 25. volume =

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Q: sin(6x) lim ? 2+0 sin(2x) Does not exist O 3

A: Given problem:-

Q: Q2: Solve the following integrals:- (2) fd 4x2-9 xp: (3)fx sin(x +1)dx

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