Find the absolute maximum and minimum points of f(x) = In (5x2 - 5x+3) in the interval x = [0,2]. Answer: Absolute maximum occurs at x = Absolute minimum occurs at x =

Q: The value of c that satisfies the Mean Value Theorem on the interval [0, 5] for the function f(x) =…

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Q: Consider the implicit equation x²2y² = 7, where y is a function

A: x2−2y2=7ddx(x2−2y2)=ddx(7)Using the power Ruleddxxn=nxn−1

Q: Given y = u3 + 2u,where u = 5 − x2, find dy/dx by the chain ru

A: Here we haveTake the derivative with respect to u

Q: Find the average value over the given interval. f(x)=x²+x-12; [0,24] The average value of f(x) = x²…

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Q: Solve the rational inequalities below. Each rational inequality will have one interval from the…

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Q: If ƒ(x) = 3x² – 3eª, find:

A: f(x)=3x2−3ex

Q: DECIDE WHETHER THE GIVEN SEQUENCE OR SERIES IS CONVERGENT OR DIVERGENT. IF CONVERGENT, ENTER THE…

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Q: Find the area of the region bounded by the graphs of the given equations. y=5x-x², y=-4x The area is…

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Q: Find the area of the region bounded by the graphs of the given equations. y=2x² -5x +9; y=x² +7x-11…

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Q: True or false: If f has a derivative at x = 2, then f is continuous at x = 2.

A: To determine whether the following statement is True or False.If has a derivative at , then  is…

Q: Differentiate the following function. f(x)=9-4x+5ex f'(x) =

A: Given,

Q: (7.3) Find the inverse Laplace transform, L-¹ 1 2s + 14 s² + 2s + 10.

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Q: Suppose a company's total cost for a product is given by C(x)=30000-60x+0.3x^2 and the total revenue…

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Q: Find a particular solution to Yp || y" - 10y + 25y = -8e5t t² + 1

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Q: A company determines that its marginal revenue per day is given by R'(t), where R(t) is the total…

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Q: dy. Simplify your answer. dx y = x³(1-x²) Calculate

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Q: Find the point at which the line {-1,-3,-5} + t{5,-3,3} intersects the plane 4x-y-z= 104

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Q: Calculate the tangent plane for the function f(x, y, z) = ecos(x)+sin(y+z) at the point (7,0,0).

A: To calculate the tangent plane for the function  at the point .

Q: Find all the values of x such that the given series would converge. ∞ n (−1)″10″ x” n=1 (√n+11) The…

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Q: Find the derivative of the function g(t) = sin (3+³+3t²). You do NOT need to rationalize nor…

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Q: Use graph below to calculate the following: (a) f(f(2)) = (b) g(g(2)) = (c) f(g(4)) = (d) g(f(4)) =…

A: A graph of the functions  and  are given.The aim is to find the composite function values  and .

Q: The graph of f(x) = 2x³ + 5x² - 5 is shown below. Use the tools to graph the line tangent to f(x) at…

A: The given function is .The aim is to find the tangent line at .

Q: Determine whether the series converges, and if so find its sum. 1 (k+4) (k+5) (Enter DNE if the sum…

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Q: Ox-2y=0

A: Given that the graph we have to find the equation of tangent line at the point origin

Q: Convert the point from cylindrical coordinates to rectangular coordinates. Зл (x, y, z)= 6, × )

A: Given  cylindrical coordinate is .We know in rectangular coordinates,

Q: Find the absolute maximum and absolute minimum values of f on the given interval. (If an answer does…

A: f(x)=−3x4−20x3 on [−7,−2]

Q: Question 25 The population of deer in a certain area of Stanly county grows proportional to itself.…

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Q: dy dx -1 Find for the function y = cot¹ √√4x². Show all steps.

A: The given function is

Q: Use L'Hospital to determine the following limit (where t is regarded as a constant): cos(wt) -…

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Q: If sin(A) = 0.59 and cos(A) < 0, determine: Be certain to express all answers to at least four…

A: Sin(2A) = 2sin(A) cos(A) Cos(2A) = cos2(A) - sin2(A)Tan(2A) =

Q: Find all absolute maximum and minimum values for the function y = 7x² + 9x +1 on the interval…

A: Given Function is as follows

Q: Given that 0. ∞ n=0 x= 1 1 - X Identify its interval of convergence. The series is convergent from…

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Q: A toy company is trying to determine the optimal price for their weekly supply to meet the demand…

A: The objective of this question is to determine whether there will be a shortage or surplus of toys…

Q: (7.1) Use the definition of the Laplace transform to find £{f(t)} for f(t) = cos(t).

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Q: Find f such that f'(x) = 4x² + 3x-3 and f(0) = 9.

A: (1) f′(x)=4x2+3x−3f(x)=∫f′(x)dxf(x)=∫(4x2+3x−3)dxUsing the Power Rule∫xndx=xn+1n+1+C

Q: Express the point given in Cartesian coordinates in cylindrical coordinates (r, 0, z). A) (³ ( ¹⁄²),…

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Q: The velocity of an object is shown in the graph below 5+ 4 Velocity (m/s) N لا 3 1 1 pasij 3 Time…

A: The velocity of an object is shown in the graph below.To calculate the total distance traveled over…

Q: (d) This graph is a lemniscate π/2 1 2 3 4 5 6 I with equation 0

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Q: m 4. Consider sin x cos" xdx. (a) How do you evaluate fsin" x cos" xdx if m is odd? (b) What if n is…

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Q: Find an equation for the conic that satisfies the given conditions. parabola, vertex (6,-3),…

A: Given the vertex of the parabola (6,-3) , horizontal axis, and passing through the point (-44,2) we…

Q: Sand falls from a hopper at a rate of 0.5 cubic meters per hour and forms a conical pile beneath.…

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Q: Find F as a function of x and evaluate it at x = 2, x = 5 and x = 9. - $² = F(x) = F(2) F(5) = F(9)…

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Q: Find the second smallest positive x-value where the graph of the function f(x) = x + 2 sin(5x) has a…

A: to find the second smallest positive value of x where tangent line to f(x) is horizontal.

Q: Given that t (a) sin(t): (b) sec(t): = tan ¹(3), find the exact value of

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Q: Find the value(s) of c guaranteed by the Mean Value Theorem for Integrals for the function over the…

A: Consider the function

Q: (4) A closed rectangular container with a square base is to have a volume of 2250in². for the top…

A: A closed rectangular container with a square base is to have a volume of 2250 in3. The material for…

Q: Suppose that Vf(x, y, z) = 2xyze¹¹i+zeªj+yeªk. If f(0,0,0) = 2, find f(3,3,4). Hint: As a first…

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Q: Let ✈ denote the vector xỉ + y j + z k and a be a fixed positive constant. Compute divF where is the…

A: Let  denote the vector  and  be a fixed positive constant.To compute where  is the vector field…

Q: 1.3 1+0.3e-4t : A bacteria is growing according to the function W (t) for t≥ 0 where W (t) is the…

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Q: 6. Calculate the domain, intercepts, horizontal and vertical asymptotes with limits, intervals of…

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