G(x) = − 1x². +3 H (x) = − 1x² – 7 M (x) = − 1x² + 1/

Q: Differentiate. f'(0) = f(0) = cos(0) sin(0)

A: Please see the below picture for detailed solution.

Q: Evaluate the given expression. Take 0-2 40-0 and C = 1 4A + 0.5C P 1 1 -1

A: We have given A=0-2-2021 and c=1-111-1-1

Q: Solve the separable differential equation dx 1 x² + 25 dt and find the particular solution…

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Q: Find an equation of the plane that passes through the given point and is perpendicular to the given…

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Q: 8. Solve the following. (a) Find the equation of the tangent line to the graph of f(x) = x²-9 at x =…

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Q: A farmer finds that if she plants 40 trees per acre, each tree will yield 20 bushels of fruit. She…

A: According to the given instruction, the answer is as follows

Q: Solve the equation for the indicated variable. R1 R2 for R₂ R₂ X

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Q: For the equation of the hyperbola: 4x^2 - y^2 = 16. Find the center, vertices, slope of asymptote’s,…

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Q: Show that the lines L₁ : x = 3-t, y = 2t, z = 2+t and L₂: x = 1 + 4t, y = 3-8t, z = 5 - 4t are…

A: Solution is given below:

Q: Consider S, the curve segment of the curve y = sin(x) from x = 0 to x = π. (a) Complete the…

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Q: Given f(x) = ln(3x2 + 8x + 2), find the equation of the line tangent to the graph of f at x = 0.

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Q: Find an equation of the tangent line to the graph of the given function at the specified point. f(x)…

A: Consider the given function. fx=5excos x

Q: D) f(x)= In x+2

A: Calculate differentiation for            f(x)=ln(x^3)/(x+2)

Q: If a ball is given a push so that it has an initial velocity of 6 m/s down a certain inclined plane,…

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Q: For the following exercises, the vectors u and v are given. a. Find the vector projection w= proju v…

A: Given: u=5i+2jv=2i+3j

Q: 1. Find the length of the arc of the curve 3 (2 x − 1)² from x = 0 to x = 8 - y = 32/2 (2x

A: Given :y=2322x-132

Q: Consider the function f(0) = 4cos2²0 + 4sine. (a) Find f'(0) = (b) Determine the critical points of…

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Q: An investment company pays 8% compounded semiannually. You want to have $23,000 in the future.…

A: given future value of investment=23000 $ interest rate=8%=0.08 time= 5 year n=2 (because interest…

Q: Use linear approximation to estimate the value of the following  cos(pi/4 +0.01)

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Q: The graph off is given. Sketch the graphs of the following functions. (Select the correct graphs.) y…

A: Transformatin rule:y = -fx :  reflect fx about x-axisy = fx + C: Move fx up C unitsy = fx - C: Move…

Q: Let a = 1 and b = 4. 0 16 S.L. ㅠ -√a²-x² If you need to use π for your answer, just type pi.…

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Q: Assume y = f(x) is defined everywhere. Suppose the point (12, -3) is on the graph of y = f(x). Use…

A: For an even function:f(-x)=f(x)   For an odd function:f(-x)=-f(x)

Q: (It sinx) dx + #* HN (It sin x) dx

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Q: I. INTEGRATING FACTORS BY FORMULA 2 1/2 x 2x/x-2

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Q: A (в C The graph of f', the derivative of the function f, is shown. Which of the following…

A: We need to choose correct option.

Q: Consider the functions graphed below. C (0,b) (1,1) (a) Find the slope of the line. slope = Answer…

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Q: Find y" by implicit differentiation. 2x³ + 5y³ = 2

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Q: A function f is given, and the indicated transformations are applied to its graph (in the given…

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Q: Use Gauss-Jordan row reduction to solve the given system of equations. (If there is no solution,…

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Q: Find the angle between the vectors. (First find an exact expression and then approximate to the…

A: Topic = Vector

Q: Find the derivate a) F(x) = 5-8x 1+ 2X f'(x)= 6) write all x-values (if any) at which the tangent…

A: (a) f(x)=5-8x1+2xd dx(ab)=bdadx-adbdxb2d dx(xn)=nxn-1

Q: Acme finds that its monthly revenue, in dollars, from the sale of x carry-on suitcases is 0.008x³…

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Q: Find an equation of the plane with the given characteristics. The plane passes through the points…

A: The given points are (3,2,1) and (3,1,-7) and plane is 8x+9y+4z=17.

Q: The sequence {an} is defined by a₁ = 2, and an+1 for n > 1. Assuming that {an} converges, find its…

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Q: Find by implicit differentia dy dx xey = x - y

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Q: Find the derivative of y = x²ª dy/dx =

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Q: Using substitution differential equations. methods to solve homogeneous Y'= Y+X

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Q: Let f(x) = 5x + 4 and g(x) = ax + c where a and c are non-zero constants. Use lower case letters in…

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Q: 2r cos 0 Replace the polar equation r= (csc 0)3e2rc with an equivalent Cartesian equation. T

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Q: 4. Suppose a balloon in the shape of a sphere is being filled at a rate of 100 ft³/min. How fast is…

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Q: Given the vector function r(t) = (4t, -³, - 3t² + 4) Find the velocity and acceleration vectors at…

A: Solution: r→(t)=4t,-t3,-3t2+4 To find the velocity vector, we take the derivative of r(t) with…

Q: What is the Point of Inflection of the following graph? 15 -0.5- O --0.5- (0,0) 0.5 (0.333, -0.296)…

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Q: Find all solutions of the given system of equations and check your answer graphically. (If there is…

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Q: A flagpole is 40 feet high and stands on level ground. A flag is attached to a 120 foot rope passing…

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Q: The functions describes the distances from the origin at time t of an object in rectilinear motion.…

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Q: Find the distance between the skew lines: z=8-9t x = 5+7t, y=3+7t, x = 1-t, y = 6, z = 5+8t NOTE:…

A: Solution:  To find the distance between the following skew lines. x=5+7t, y=3+7t,  z=8-9tx=1-t, y=6,…

Q: Find an equation for the graph sketched below: -5-4-3-2 ME 6 S -2 -3 -4. 5 -6 -7 -8+ N a

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Q: Use f(x) = x - bln(x) to answer the questions below. Assume b is a positive constant and x > 0. (a)…

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Q: Locate all the critical points of the function f(x,y)=8x−x^2−4xy^2.

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Q: Consider the following equations. f(x) = √x + 5 g(x) x+5 Sketch the region bounded by the graphs of…

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