Question 1: Let f(x) = x³ - 3x² +4. a) Find the intervals of increase and decrease. b) Find the local maximum value(s) and local minimum value(s). c) Find the intervals of concavity. d) Find the inflection point(s).

Q: A twice-differentiable function f is defined for all real numbers x. The derivative of the function…

A: Given: A twice‐differentiable function f is defined for all real numbers x. x 0<x<3 3…

Q: Write the given function as the composition of two functions. y = -√√14+4) 4x Choose the correct…

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Q: 4. Using a graphing calculator or software, graph the following system of nonlinear equations and…

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Q: Let a . Find a unit vector in the direction of a = 1 35 i + 5 √35 =j+ k 3 35 X Invalid notation.

A: Let's find unit vector in the direction of a.

Q: f(x) 0, =4-x², 0, 0<x<2 2≤ x < 3 x ≥ 3

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Q: Find the projection of the point (-8,2,3) onto the zz-plane.

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Q: Evaluate the limit using L'Hôpital's Rule: Is it an irrational number? limo+ (1 + x)²

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Q: 2 + 4 + 6 +...+ 2n = n(n + 1)

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Q: Use logarithmic differentiation to find the derivative of xsinxe2x+3 cos² x y =

A: Topic:application of derivatives

Q: Solve Bernoullis Equation. dy dx + 51x 11 y³ X 3

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Q: Use induction to prove that for all n E NU {0}, 3n < (n + 2)!.

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Q: Problem 4 lim Δx + 0 sin( (5)+Δx) - () Δ.χ

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Q: Derive term by term the Maclaurin series (Taylor series around the origin) of the function sinh(z)…

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Q: دان دام 0 → --2 +1 0 1 Graph of f 4 5 Based on the graphs of function f and function g, determine…

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Q: a plane through the points (1,8,-8), (-5,7,1), (1,-3,-6) = +12y + z = -335 X

A: We will find the required equation of plane.

Q: Question 2: Evaluate the following integrals. Show your work for full credit. Lax (lx) + 3) dx

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Q: Solve the differential equation or initial value problem. (1) 2ye'y' = 2x + 2x + 3√x

A: As per our guidelines we can answer only 1 question so kindly repost the remaining questions…

Q: 1. Given a circle with equation (x + 1)² + (y − 2)² = 8, find the a. Center b. Diameter 2. Find the…

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Q: Find an equation of the plane that is parallel to the plane x + 5y - 10z+15= 0 and contains the…

A: Given :x+5y-10z+15=0point 5, 1, 6

Q: Find the distance from the point (-7, 6, 8) to the x axis.

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Q: Use part one of the fundamental theorem of calculus to y = 3x + 7 t 1 + 1³ dt

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Q: If vectors u and are parallel, which of the following are TRUE? O and must always be drawn on the…

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Q: Find the required higher derivative. Show your complete solution. 1. x=a²b sin at y = ab² cos at ;…

A: The given problem is solved below in detail.

Q: 4) Generate the solution of the DE 24 cx2 + 649 = sin(4x)

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Q: (b) Find the general solution of the inhomogeneous second-order linear ODE 2y" - 5y3y = 10 sin x.

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Q: O-0.25 0 Functions f, g, and h are functions of x. Use the table to find lim h(x). X-0 x -0.1 -0.01…

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Q: 9 The acceleration of a lift in a tall building is ½(t – 5) m/s² at time t seconds. At time t = 0,…

A: We have to find the number of floor at which the lift stops.

Q: 07* 1. Find the general solution of the differential equation (Only the homogeneous part) y = A +…

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Q: (4) If y ==, then y' = x3 ex (A) (B) 3x²-x³ e4x (C) 3x²-x³ 2ex (D) (E) (F) 3x²+x³ e2x 3x²-x³ e2x…

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Q: Let y = 2(x – 3)2 – 6. Part A: Is the given relation a function? Is it one-to-one? Explain…

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Q: Use a software program or a graphing utility with matrix capabilities to find the determinant of the…

A: 971-20-105140947-3127-9824-204

Q: Show that fsint dt = using Laplace

A: To prove:- ∫0∞sinttdt=π2

Q: Graph the curve r² = 4 cos 0

A: the required graph is difficult to draw by hand so  I have attached the picture  of  r2=4cosθ

Q: Find the area of the indicated region. Enclosed by y = Inx and y=2x-3. (Round answer to four…

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Q: Determine which property of determinants the equation illustrates. 2 2 4 = -1 O If one row of a…

A: We have to determine which property of determinants the equation illustrates.

Q: 9.- A market analysis reveals that the profit P that a store will obtain with a certain item depends…

A: 9.- A market analysis reveals that the profit P that a store will obtain with a certain item depends…

Q: Find the arc length of the graph of the function: A B D E 17 12 15 8 49 12 49 24 15 4 = + 2x2 over…

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Q: The series e² = 1 + x + + 2! 3! converges to e for all x. a. Find a series for (e). b. Find a series…

A: Given, ex=1+x+x22!+x33!+x44!+x55!+⋯ converges to ex for all x.

Q: Written Activity 1. Determine the center and radius of the circle with the given equation. a. (x +…

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Q: Find the orthogonal projection of y= 4 on W (10) Span

A: To Find : 0rthogonal projection of y=641 on W=Span-4-11 ,011

Q: lim Δx - 0 COS(π+Δx)+1 Δε

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Q: f(x) = x² – 2x²

A: Please see the below picture for detailed solution.

Q: 1. The inverse demand function for a certain product is given by the function p = f(q) = 26q/40,…

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Q: Find the area of the indicated region. Enclosed by y = 2x + 1, y = 3x − 1, x = 0 and x =2. (Round…

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Q: is taxed at 22%. Which equation represents the amount of tax owed for x dollars of income? (0.12x…

A: Topic:- application of algebra

Q: Find sets of parametric equations and symmetric equations of the line that passes through the given…

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Q: -7 and g(x) or (f(u)). Do not expand your answer. te the ful g(f(u)).

A: We will find the required.

Q: Find the antiderivative F(x) that satisfies the given condition. F′(x) = −5ex+5x; F(0) = −6 F′(x)…

A: The given function is F'(x)=-5ex+5x,     F(0)=-6

Q: The following is the graph of a function f(x). -5 -4 -3 -2 -1 Clear All Draw: 4 3 2 -1 -2 -3 2 a. On…

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Q: Find an equation of the plane that passes through the point P(5, 6, 3) and has the vector n = (1, 9,…

A: To find an equation of the plane that passes through the point P5, 6, 3and has the vector n=1, 9, 9…