Suppose that f(x) = 6x + 3x². Evaluate each of the following: ƒ'(2)= f'(-1)=

Q: Use the method of variation of parameters to determine the general solution of the given…

A: Determine the general solution of differential equation…

Q: 1. f(x)=x²+2x+1 & f(x) = 2x+5

A: To find the area between the curve.

Q: Consider the vector function r(t) = . (a) Find the unit tangent and normal vectors of r(t).…

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Q: y=1/(AX+B) Make a differential equation

A: Given :y=1Ax+B

Q: 3 Detennine it the following series is on divergent Convergent a 745-6 นะ ET 3n³+2n Determine if the…

A: Series Divergent Test : Consider the series ∑n=1∞ an . If limn→∞ an does not exists or non zero .…

Q: Consider the following. y = x² y = 12 - x K 16 14 12 -2 10 B 6 4 2 2 8 10 12 (a) Find the area of…

A: To find the area of given region.

Q: f'(x) = -2 sin(x), ƒ(4) = √² +7

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Q: A pilot is flying from Daytona Beach to Prescott. The two cities are 1874 miles away from one…

A: Let speed of light  = Va         wind speed  = Vw = 12mph  let flight flying direction WαN       ⇒…

Q: If the angle of the moon is decreasing at 0.25 radian per hour, how fast is the shadow of a 150 ft…

A: If the angle of the moon is decreasing at 0.25 radian per hour, to determine how fast is the shadow…

Q: Find the relative maximum and minimum values. f(x,y) = x² + xy + y² -34y +385 Select the correct…

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Q: = 4. Consider the function f(x) = 1 x² - 1 a. Find the intervals f is increasing. Find the intervals…

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Q: For every 2 x 2 matrix A, we have det (A)² = (det (A))². O True O False

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Q: Evaluate 5x e (e5x+3)⁹ 9 dx

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Q: f sin³ ycosydy

A: I have stated the used formulas in the solution

Q: Determine the domain of the function of two variables f(x,y)=√√y + 3x. The domain is {(x,y). (Type…

A: To determine the domain of the function of two variables fx, y=y+3x.

Q: Question 10 of 10 Sketch a possible graph of a single function satisfying all of the following…

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Q: Part II (10%) - True or False. For each statement, select T if the statement is true, or select F if…

A: Given question:-  For each statement, select T if the statement is true, or select F is statement is…

Q: You are planning to make an open rectangular box from a 38-in-by-75-in. piece of cardboard by…

A: This question is based on application of derivative.

Q: Find the general solution of the differential equation. y (4) + 2y"+y = 9+ cos(4t). NOTE: Use C1,…

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Q: Find the solution of the given initial value problem: y(4) + 2y"+y = 3t+8; y(0) = y'(0) = 0, y"(0) =…

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Q: Find y' if y= 8 3 7x

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Q: Speeding up

A: the answer is 173 yard/sec , since speed is positive the humming bird is speeding up

Q: 3. The value of A. B. C. D. [xsản xdx (1 - x²) 3/2 + C -sin-¹ x - √1 − x² + ² - (1-x²) ³/² + C sin-¹…

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Q: Evaluate f cos*x sin² xdx. 1 16 A B O A 1 -x+ sin 4x 48 1 =x+ 16 1 8 sin 4x 1 64 1 sin³ 2x + C sin³…

A: We need to evaluate integral.

Q: 5. S dx xlnx

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Q: Use Lagrange multipliers to find the indicated extrema, assuming that x, y, and z are positive.…

A: Given that , fx,y,z=x2+y2+z2 and constraint is x+y+z-27=0 find the extrema using Lagrange…

Q: state the domain and range for each of the following:

A: Given set of points S={(-3,-2),(-2,-1),(-1,0),(0,1),(1,2),(2,3),(3,4)} We know that domain is the…

Q: Find the solution of the given initial value problem 150y" + 25y" + y′ = 0, y(0) = −14, y′(0) = 10,…

A: We know that the solution to 150y'''+25y''+y'=0, y0=-14, y'0=10, y''0=0 will be…

Q: Sketch the region that corresponds to the given inequalities.   12x  +  6y ≤ 60   6x  +  12y ≤ 60…

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Q: A function is given. g(x) = 7 +  1 2x;    x = 1, x = 7   (a) Determine the net change between the…

A: Given the function gx=7+12x , x=1, x=7

Q: 3. Find the absolute maximum and absolute minimum of f(x) = 2x³ - 6x +1 on [0,3].

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Q: $fº f(x) dx = 12.5. Use this information to fill in the blanks. (Round your answer for part (f) to…

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Q: Evalua COS [cas (VF) ². √t = √t

A: We have to integrate the given trigonometric term.

Q: Find all relative extrema and saddle points of the function. Use the Second Partials Test where…

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Q: Suppose g(x) is differentiable at x = −7, g(−7) = 4, and g'(-7)= 2. Select all statements that must…

A: Suppose gx is differentiable at x=-7, g-7=4, and g'-7=2.To determine the true statements that are…

Q: Determine if each of the equations given is or is not exact; Solve those that are exact. a) (x +…

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Q: Find the areas of the regions enclosed by the following curves. (a) r= 1+2cosł

A: Given :r=1+2cosθ

Q: Test the series for convergence or divergence. 8 Σ· n = 1 2 n

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Q: #3. Find the limit of the {√ 1 1+ 3n n 8 n=1

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Q: jw)² +5jw+6 =(jw)² +3jw+2jw +6 =jw(jw + 3) + 2(jw+3) (jw+3)(jw+2)

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Q: 7. f sin4xdx

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Q: 3. Find the volume of the solid of revolution formed by revolving the region bounded by y = x - x³…

A: To find out the volume of revolution.

Q: Evaluate the limit using the Basic Limit Laws and the limits limx→explq = cp/q and limx→ck = k.…

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Q: 4. Let f: [a, b] → R,g: [a, b] → R, and x E [a, b] such that f'(x) and g'(x) exist, g'(x) = 0, f(t)…

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Q: 8. f(sin3x – cos4x) dx

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Q: Determine whether the series is convergent or divergent. Σ Στ Σ n = 1 +4

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Q: = f f(t) [ ³wt e dt fat. ejut dt How did he get the limits of integration?

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Q: Find the Wronskian of the functions f(t) = 4et sin(t) and g(t) = et cos(t). NOTE: Your answer must…

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Q: 6. Find the equation of the tangent plane to the surface: ==√√4-x²-2y², at (1,-1, 1)

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Q: Find the four second-order partial derivatives for f(x, y) = 2x³y² +6x5y4. fxx² fyy= x" fyx 11 11 11

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