1. Explain in full sentence(s) using the Intermediate Value Theorem why the equation 4x³ + 3x - 2 = 0 has at least one solution in the interval [-2, 2].

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Q: 1) Using Euler's formula prove the following: For any ZEC a) For Sin² z + cos² z = 1 2 b) For any…

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Q: (a) the largest possible volume. (b) The smallest possible volume. 8-2x 8-2x

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Q: Find the linear approximation of the function f(x, y, z) = your answer to five decimal places.)…

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Q: Find the following. If no value exists, enter DNE.

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Q: Find the volume of the area bound by y=x^3, y=0 and x=1 if rotated about x=2.  Use washer method.

A: Region is bounded by y=x3,y=0,x=1Rotating the region about x=2x=y1/30≤y≤1Using the washer method

Q: Conclude that the sequence (an) is a decreasing sequence, where 1 2 1 an = 1+ +.... + - In n. n Draw…

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Q: z-6 Consider the function f(x) = 7+6) Of(x) has an oblique asymptote f(x) has a vertical asymptote…

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Q: Find the general solution of the differential equation: dy - 2ty + 4e¯t². dt What is the integrating…

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A: First, we will understand the concept of limits.Let us consider a real-valued function “f” and the…

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Q: Consider the region in Quadrant 1 bounded by y = x^2 +1, y = 5, andthe y-axis. Find the volume of…

A: The objective of this problem is to find the volume of the solid obtained by rotating the region…

Q: Problem 134. Find the antiderivative family for the function y = sin² (x) cos² (x). f(x) =

A: Given,

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Q: Help find a function f so that f ‘(x) = 3x2+ 2x+5 and f (1) = 10

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Q: Evaluater(g(t)) using the Chain Rule: r(t) = (et, e³t, 1), g(t) = 3t — 2 #r(91)) = (100

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Q: h(s)=-2√s S

A: X Intercepts: (0, 0), Y Intercepts: (0,0)Asymptotes: NoneExtreme Points: Maximum (0, 0)

Q: Suppose your demand function is given by D(q) = -q^2 -2q +585, where q is thousands of units sold…

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Q: . An airplane has a ground velocity of 400 km/h, [N60OW]. The plane is affected by a90 km/h wind…

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Q: Let f be a differentiable function such that f(1) = −3 and f'(1) = -9. What is the approximation for…

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Q: Consider the following. y=x³-3 3x² + 5x + 3 Find the relative maxima, relative minima, and points of…

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Q: 4. A marine manufacturer will sell N(x) power boats after spending $x thousand on advertising, given…

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Q: Evaluate SSS x²dV, where E is the solid lies within the cylinder x² + y² = 1, above the plane z = 0,…

A: To find:- , where E is the solid lies within the cylinder  above the plane  and below the cone

Q: 1. Given that lim f(x) = -8 and lim g(x) = 3, find the following limits. X-2 x-2 (a) lim (4f(x) -…

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Q: 5x 1. f(x) = x²-4 Analysis x-intercept (s): y-intercept: domain: range :

A: Given that the function      x-intercept(s):To find the x-intercept, set           y-intercept(s):To…

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A: The given rational function is

Q: Given the graph of f below -3 -2 -I--x -1 (2) lim f(x) x-2+ 5+y 4 3 2 0 -1 answer the questions…

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Q: The function C(t)=C0(1+r)^t models the rise in the cost of a product that has a cost of C0 today,…

A: The Present cost of boat is The Average inflation rate is  for 2 yearsTherefore, we have to find the…

Q: Find the velocity, acceleration, and speed of a particle with position function r(t) = (-3t sint,…

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Q: 1. Find the positive number(s) b such that the average value of y = 2 + 7x-x³ on the interval [0, b]…

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Q: If an object's position over time is given by the function d(t) = (t² + 3)e for t > 0, on what…

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Q: For this exercise, refer to the cost and revenue functions to the right. The cost of producing x…

A: Consider the given figure below:

Q: Consider the functions f(x) = x² and g(x)=√x. (a) Find f/g and its domain. (+)(x) = Domain: Ox≤0 O x…

A: The objective of this question is to find the quotient of two functions, f(x) and g(x), and their…

Q: Find the area under the curve y = f(x) = x³ over the interval [5, 6]. Enter the exact answer. Area

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Q: then A-¹ = A = [ 3² ],

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Q: Help plzzz

A: The objective of the question is to determine whether the given series converge or diverge using the…

Q: Complete the table of function values. Do not use a calculator or tables. Evaluate the six…

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Q: Consider the following function. y= = ²³+2/2²- - 2x + 7 (a) Find y'= f'(x). 2 F'(x)=x²+x-2 (b) Find…

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Q: 17) Calculate the indefinite integral S-5dx √4-16x² 16) Evaluate the definite integral Š - 0 3…

A: 16).17).

Q: Consider the following. f(-4)=-7, f(1) = 4 (a) Write the linear function f that has the given…

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Q: Consider the following. f(-4)= -7, f(1) = 4 (a) Write the linear function f that has the given…

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Q: The function f(x) = 2x³ + 9.48x² +92.8872x - 0.89 is increasing on the open interval ( It is…

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Q: Solve y" 10y' + 21y = 0. -

A: The given differential equation is

Q: Let f(x) = x². There are two lines with positive slope that are tangent to the parabola and that…

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Q: Given f (x, y) = 2x6 - 3x²y² + 3y5, find fz(x, y) = fy(x,y)= fzz(x, y) = fry(x, y) =

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Q: Given lnln2equals=0.6931 and lnln5equals=​1.6094, find ln left parenthesis 4 e right…

A: The objective of this question is to find the natural logarithm of 4e using the given values of…