Use mathematical induction to prove that, for n≥ 1, n³-n is divisible by 3. Note: If you would rather show your work on a separate sheet of paper, you may up- load your work in Question 12.

Q: State the domain for the function f(x) = log(x) - 1: O (-00, -1) O (0,00) O O (-∞0,00) (-∞0, 0)

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Q: 2. Find the limits. Show your side work. 2 x-2 (x - 2)² (a) lim (b) lim tan x I→π/2- (c) lim tan x…

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Q: Item 3 If f(x) = 2x² and g(x) = 1. (fg)(-3) II. (f- g)(2) 9 IV.(ƒ + g)(1) 0.5 108 The largest value…

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Q: What is the smallest value of the number n so that the graph of the following function have a…

A: f(x)= (-2x4+1)/(6xn-3x2-1)We have to find smallest value of n for f(x) has horizontal asymptotes

Q: A contour map for a function f is shown. Estimate the value of f(1,12) 30- 20 10- 70 140 2 210 3 280…

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Q: A cubical box has interior measurement of exactly 3 meters long along  each edge. If the material…

A: To approximate the volume of the material used in constructing the box, we can consider the…

Q: Find r(t) and v(t) if a(t) = tk, v(0) = 7i, r(0) = 4j. (Use symbolic notation and fractions where…

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Q: Given the Pythagorean theorem a² + b² = c² where a and b are the lengths of the perpendicular sides…

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Q: Let g(x,y)= ln x + 2 ln y-x-8y Find the critical points. Then determine if the critical points are…

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Q: The family of curves represented on this graph would appear to be consistent with which of the…

A: Y

Q: Rewrite the following equation with the variables separated. y' = 6xy² + 2xy + 6y² + 2y

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Q: 2. Given that p = (5,-2,4), q = (3,-4,-2), and'r = (-3,2,1), calculate the following. c) pxr d) the…

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Q: Assignment: Find all exact solutions to the following equations: 2e (3x+5) cos(x³ + 1) = 0 Include a…

A: We will set each factor on the left side of equation equal to zero to solve the equation.

Q: Evaluate the line integral Jc (2x³y³) dx + (9x³ + y³) dy where C is the unit circle, and verify…

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Q: 2. Determine the Cartesian equation of the plane containing these lines: z+2 x-5 z+5 3 and L₂: *5 =…

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Q: The velocity of a particle on the x-axis is given by the differential equation dx d=³√t, The…

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Q: At an Oregon fiber-manufacturing facility, an analyst estimates that the weekly number of pounds of…

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Q: the equation F(x,y,z) = 0 determines z as a differentiable function of x and y, then, at the points…

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Q: Change the Cartesian integral into an equivalent polar integral. Then evaluate the polar integral. 9…

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Q: 12. Compute the derivative of f(x)= = (a) The quotient rule (b) The product rule I for constant n…

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Q: Find functions f(x) and g(x) so the given function can be expressed as h(x) = f(g(x)). (Use…

A: Here the given function is .Required :We have to find two non-trivial functions for which .

Q: Find all the local maxima, local minima, and saddle points of the function. f(x,y) = x³+y³…

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Q: 9. Find the points on the graph of y = to the line 28x + 50y - 17 = 0. 7x x-2 where the slope of the…

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Q: 20. If f'(r) exists at r= a, then (A) True (B) False lim f(x) = f(a) PTA

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Q: Determine vector and parametric equations for the line with z-intercept 4 and is parallel to the…

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Q: 3. Differentiate and simplify in fully factored form. a) f(x) = (1+x²2) 3 b) y = (3x² + 4)²(3 + x³)5

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Q: So dt = 1+14 A. B. C. 11/12 71 N|T (x²) arctan (x4) arctan ½ ln (1 + x ¹ )

A: Given integral

Q: Solve the differential equation with the given initial condition. dy sin x dx y+2' y = with y(0) = 3

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Q: S sin x cos²x+cosx dx

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Q: It is determinate because there is only one known force. It is determinate because there are no…

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Q: a- what is the difference between derivative of X^n and y^n (explain the followings: how many terms…

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Q: Let f(x) = In(x) and g(x) = log3x. For all x>1, f(x) < g(x) O True O False

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Q: The graph shows the velocity v(t) of an object. 4 3 2 1 0 1 O 13.5 O 14.5 O 15 2 3 O 15.5 4 V(t) 5 6…

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Q: Consider the curve y = x² + 3x + 5. Find the slope of the secant line at the point where x = 9. Oh…

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Q: 4. Find the local extrema for the given function below. No graphs. f(x) = x + ln(x² + 1)

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Q: 7. Identify if the statement is Always True, Sometimes True or Never True. If lim f(x) exists, then…

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Q: Find the slope of the curve y = cos The slope of the curve is (Type an exact answer.) ¹x at √3 T 2'6…

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Q: Simplify the following expressions. sin x sec x sec² x-tan²x+cot² x sin² x cos 2x-cosx sin 2x+sin x

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Q: Find the first partial derivatives of the following function. 8u 5v + 7w F(u,v,w)= F₁ = Fu

A: given

Q: Find all the second-order partial derivatives of the function f(x,y) = 3x + 1y+2: 2²f 11 ах'…

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Q: , find the range of the function f(x) = 2x² + 12x – 3.

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Q: Consider the following integral. Sketch its region of integration in the xy-plane. (a) Which graph…

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Q: lim x-o X 2e²x 2е 'te +2 Зезу зе 3х2х c2x +5

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Q: 5C AND D

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Q: Q9. Water is brought to a boil and then removed from the heat. The temperature, T, after t minutes…

A: Water is brought to a boil and then removed from the heat The temperature , T after t minutes is…

Q: Q6. The population of foxes in a provincial park is modeled by the equation P(t)= +40, where t is…

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Q: From the graphs of f and g in the figure, we find the following. (Assume that each point lies on the…

A: Given:We are required to find:

Q: Given f(x) = 2x² + 1 and g(x) = 4x - = 4x - 6, find the following. (a) f(g(2)) (b) f(g(x)) (c)…

A: Given functions are,Under guidelines we are suppose to answer only 1 or 3 sub parts.

Q: f = -9i+40j Find: -9f f=i-j g=12i+ 3j Find: -4f-10g u = -9i+4j Find: -5u

A: “Since you have posted a question with multiple sub-parts, we will solve first three sub parts for…

Q: The plane x + y + 2z = 10 intersects the paraboloid z = x² + y² in an ellipse. Find the points on…

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