Which Theorem states: If f is continuous function on the open interval (a, b) then f attains an absolute maximum value f(c) and an absolute minimum value f(d) at some numbers c,d in(a,b) is: A. The Extreme Value Theorem, B. The Intermediate Value Theorem, C. The Mean Value Theorem, D. Rolle's Theorem, E. None of these

Q: A. Evaluate the following integrals. dx 1. 5+x² dx V4-9x² dx x V16x2-25 dx 4. x2+4x+13 2. 3.

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Q: Select the answer option that corresponds with polar coordinates (3, –150\degree). 90° 2 W/12 134…

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Q: Find the function f given that the slope of the tangent line to the graph of f at any point  (x,…

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Q: dx V4-9x2

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Q: Find the principle solution of tan(4 – 4x)= 0. %3D

A: find for x tan(4 - 4x) = 0 4 - 4x = tan-(0)              [ take both side tan inverse 4 - 4x = 0…

Q: x²+6x , |2x-4 , x<a Find all values of a such that the function, g(x)= is continuous xz a…

A: g(x) is continuous everywhere if it is continuous at x=a as…

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Q: 3. Evaluate the following integrals: cos e OP (1+ sin 6) Vsin e G = H = sin (-9x) dr I +1 dr 1² In…

A: We have to find the integrals.

Q: if 0 < x < 5, if 5 <x < 10. За-15 f(x) 15 - За Evaluate the definite integral by interpreting it in…

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Q: Choose the point which shows the correct location for the polar coordinate (1, 320°). 90° wIN 135°…

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Q: dx V5+4x-x² 5.

A: We have to solve question  5

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A: f(t) = -34t + 285 this is velocity function for the distance we have to integrate the function s(t)…

Q: Select the answer option that corresponds with polar coordinates (1, -). 90° W/2 150° 45 1 7 radians…

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Q: Find Jul, Ivl, 12ul, , lu + vl, lu - vl, and lul - Ivl. = (6, -7), v= (-3, -3) u Jul |v| = |2ul =…

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Q: x = r° +1, y=r² -t a) Find dy/dx Show all your work.

A: x =f(t)dxdt=f'(t)   y=g(t)dydt=g'(t)Then,dydx=dydtdxdt =g'(t)f'(t)

Q: For each of the following, solve exactly for the variable z. (a) 1 -+-. 0.3 (b) - +- 0.5

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Q: Direction: Prove using the three conditions of continuity if the following function is continuous or…

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Q: 7)S ) dx 8)S; dx 1+3e* 9) S 3x3. e-2x* dx

A: As per our guidelines we are supposed to answer only first three parts. Kindly repost others…

Q: 1. Find the antiderivative of 3.x² + 2? 2. How do you find the antiderivative of a given function?

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Q: 1. m(t) = -6t(5t* – 1)* 2. y= (x3 + 2)(x² – 1)* 3. y= (x - 8)* (x +3)5

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Q: Show that the production function f (x) = - () x3 + 10x? + 5x, -∞< x< ∞ has both a concave and…

A: Find your answer below

Q: The inflection point of the function f(x) = x³ – 4x² + 4x + 2 is: (금, 끓) 3 7 4 ' 27 7 (금, 꽃) 4 70 3'…

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Q: 4. Sketch the function Ax) = 2xª – 16x², indicating any extrema, points of inflection,

A: follows the procedure given below.

Q: Find the indicated value. Use special angles, together with the fact that z is the period of the…

A: We have to find the value of cot

Q: D(X) is the price, in dollars per unit, that consumers are willing to pay for x units of an item,…

A: Here, the given functions are: D(x)=100x, S(x)=x

Q: Use the zero or root feature of a graphing utility to approximate the zeros of f(x)= 2x³+8x² – 5x-7…

A: The objective of the question is find the roots (zeros) of the given function.

Q: 2. Evaluate the indefinite integrals: D = tan r secʻ r dr 8x + 7 dr 72 +1 E = - 2dr F = dr V9 - 36x2

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Q: What is the area of the region between the graphs of y = x – 1 and y : -X – 1

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Q: | (3y + e?v=) dx + (4x + 4 cos (y°)) dy. Use Green's Thoerem to evaluate the line integral x² and x…

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Q: Find T(t) and N(t) at the given point. r(t) = 2 cos(t)i + 2 sin(t)j + tk; t = 2 T -25 i + 15 k NE) =…

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Q: a?u 2. Solve 0, 0 < x < T, 0 <y<n, + и(0, у) %3D 1, и(п, у) — 1, 0 < y< n и(х,0) — 0, и(х, п) — 1, 0…

A: Solving

Q: II. Given the function g defined by g(x) = -* if x*-2 4. if x=-2 Find the value of the indicated…

A: at x=-2, function is defined as:g(x)=-4;       if x=-2ANSWER 14:g(-2)=4

Q: x² 4x + 5 lim 3x а. x+5 lim b. x+7 x² - 49 x - 7 lim С. x² - 3x + 2 2 - 4

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Q: Find the area of the region in the xy-plane bounded above by the graph of the function…

A: Given  fx=711x-2111, x=3 &amp; x=14 To find Area:

Q: 2. Let A = (1,0, 2) and B = (6, –2, 3). Solve for projĄB.

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Q: 13. Evaluate the given integral, ſ t (t² – 9)i: A. (1² – 9)* + e 3 . (t2 -9)호 + c В. 3 C. · (t² –…

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Q: Drection: Evalate /(2) fr the gien functons. a. -2 b. -6 d. 2 4 f)=P-4 a. 3 b. 6 c. 12 d. 2

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Q: correct position in the answer box. Release your mouse button when the item is place. If you change…

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Q: Find the particular solution determined by the initial condition. 2/3 f'(x) = 3x - 6x; f(1) = - 7…

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Q: Simplify the expression. sec @ — csc ө 2) sec 0 sin 0 – cos 0 csc 0

A: Simplify the expression

Q: Express f(x) in the form f(x) = (x-k)q(x) +r for the given value of k. 3 f(x) = 3x +x +x-4, k= - 1…

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Q: Find the intersection of the line and plane: 2x + 4y – 3z = 19, r(t) = (-2, 1, –1) +t (1, –1,2)

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Q: differential eqation, find general solution for dy/dt = −3y + 4 cos 2t   thank you.

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Q: State sec(cosec÷) in terms of x. Hence solve the equation 1 sec(cos ec 1 2x

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Q: Convert the Cartesian coordinates (2, -2) to polar coordinates. (2√2, 300°) (2√2, 315°) (2√2, 330°)

A: To convert the given point from Cartesian to polar coordinates.

Q: Is the polynomial in standard form? [ Select] Classify the polynomial by degree [Select] * and…

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Q: Use the method of Substitution to integrate the following 5s * e^(s^2+4)

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Q: the area of the region enclosed by y = 2 – x´ and y = -x, identify the "a" and "b"

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Q: y = sin(x), y = 2x

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Q: 1. Consider A = (0, 4, 2) , B =, (6, –1,0) and C = (3,0, 1). 1 (a) Find the unit vector having the…

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