Let f(x) = 5x4 - -1/2+8√x-3. (a) Find f'(x). (b) Find an equation for the tangent line to the graph of f(x) at x = 1. 5.

Q: E Eo A formula for calculating the magnitude of an earthquake is M = log that uses the common (base…

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A: Given query is to find indicated limit.

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A: y= (t tant)11 y= t11 tan11tUsing formula ( d(uv) = uv'+vu' )diff w.r.t "t"dydt=t11.11tan10(t) sec2t…

Q: 2 3s +9 Option 3 23 -e³t e-3t Option 4 None of the choices Option 2 Option 1 2 -3t 3 3 N|W 2 co

A: As we know the inverse Laplace transform identity; L-11s-a=eat   Given: Fs=23s+9

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Q: In the following problem, begin by drawing a diagram that shows the relations among the variables.…

A: Use partial derivatives

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A: Follow the procedure given below.

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A: Here we have ∑k=1∞2+(-1)k5k

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A: Note:- As per our company guidelines we are supposed to answer only first three sub-parts. Kindly…

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Q: Use integration by parts to show that [x²³e³x² dx = 1 50 est (5x² −1)+c

A: ∫x3e5x2dxSubstitute u=x2→dudx=2x→dx=12xdu=12∫ue5uduIntegrate by parts:∫fg'=fg-∫f'gLet f=u and…

Q: Obtain the general solution unless otherwise instructed -24 y'"' + 4y″ + 9y' + 10y = ² when x = y =…

A: Given

Q: Evaluate the following integrals: 4x 6. ²x3x²y²dy dx 7. p² sin 0 d0 dp Ꮎ dᎾ π/3 π/6 8. (2-y)dy dx 9.…

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Q: S52² +32° +22²-32 +2) dz

A: Solving the problem by finding the value of integration.

Q: Given R(t) = 4 costi + (1+3cost)j +5sintk. Find B(t) att = 7. 3 B (t) = 3/1 - k i- B (t) O Option 1…

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Q: find the distance from the point P (2,1,1) to the lins x+1 y-1 Z-3 L: 6 -2 -3 = =

A: To find the distance from the point to the line.

Q: Q2/Find the value of the integral dx 1+x² by using simpson method (n = 6)? 3

A: Find out the value of the integral using the simpson 1/3 method.

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Q: 9. (20 pts) Find the area between (bounded) by the curves y = x² + 10x and y=2x+9.

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Q: If f is a differentiable function and f'(x)=x55x4+ 5x³+2, then f is concave up on

A: As per our company guidelines we are supposed to answer only one question. Kindly send other…

Q: 46 0-25 A= ,0 01 Find all the eigenvalues of A. For each eigenvalue, find an eigenvector. (Order…

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Q: Find the determinant by row reduction to echelon form. 1 3-2-4 01-25 -1 1 2-8 6 4 -2 -3 3

A: 1. Row echelon form

Q: 3. y²(x + 2y) = 8

A: The Solution is dydx=-y2(x+3y)

Q: Water is pumped into a sphere at a constant rate as seen on the figure.

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Q: 2) Find the average value of the function f(x, y) = 6x + 4y over the plane region R. defined by the…

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Q: ind the average value of the function f (x, y, z) = x² + y² +2²³ over the rectangular prism 0≤x≤ 5,0…

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Q: Q3/Find the value of x If the approximation of the integral ſ f(x) dx by trapezoidal method is given…

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Q: gh (2,-5), parallel to y= 2x+4

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Q: dx 9-x

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Q: 2) lim f(x) if f(x) = {x²43) X2² fx²-9, x2 x-2 F(x) X 2.75 2.5 2.1 2.01 2.001 X 1.5 1.75 1.9 1.99…

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Q: 1. Describe the transformations of the graph of y=√x to obtain the graphs of the following…

A: see below the answer

Q: Evaluate lim √9-t-3 t-o t

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Q: Use Taylor's formula for f(x,y) at the origin to find quadratic and cubic approximations of f near…

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Q: In(x²y)- ez-tan"¹ z. Assuming that z is a differentiable function of x and y. Let F(x,y,z) Find F.…

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Q: 19. Find potential function for = (3xy, æ³)

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Q: -4 -3 -2 -1 wo 4 -1 -2 -3 -4 -5 1 2 3 4 5

A: Slope is given.

Q: Consider the matrices shown below: Compute CT-A 3 07 A = -1 2 E -B C = 13] 3 1 5

A: Given: A=30-1211, C=142315

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Q: Find all critical points of f(x) = 3 + 12x - x² and use the First Derivative Test to determine…

A: Given function f(x)=3+12x-x2 To find critical points we need to differentiate the function f'(x)=0…

Q: A. Find the general equation of the conic with the given properties. A hyperbola with foci at (4-…

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Q: hat are the cylindrical coordinates of the point whose spherical coordinates are

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Q: Is it possible to solve all the points with Finding Domain and Range 1) y sin x 2) y = cos x J= tan…

A: Solution is given below

Q: We start from the expression for the contact force 4 a³ 1/21 F=E (₁ 7² - (07*³²¹) ³²) '8γπa3 E* 3 R…

A: We have to find the differentiation of the above equation.

Q: solve the differential equation 2) 2x² dy dx csc (X)

A: