35) Differentiate a) f(z) = (1-e²)(z + e²) b) f(t) = t³+3t t2-4t+3

Q: For f(x)=√16-2x (a). find the domain. Write your answer in interval notation. (b). Graph f(x)=√16 -…

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Q: 24) Evaluate the limit, if it exists. If it does not exist enter DNE. x²-3x² + x lim x-00 x³x+2

A: (24) L=limx→∞x4−3x2+xx3−x+2

Q: Evaluate the indefinite integral: ST 7xe² dx = = + C.

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Q: 4. Jose <<= 900 100 Let e be an angle in standard position with the point (-4,-3) on its terminal…

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Q: Determine the volume of the solid generated by rotating function f(x) = √64 - ² about the x-axis on…

A: The given function is

Q: Consider the following. f(x, y) = 8x 9y (a) Find f(7,4) and f(7.1, 4.05) and calculate Az. f(7,4)…

A: Consider the following.(a) To find .(b) By using the total differential   to approximate .

Q: The graph of f(x) is shown below. Estimate and list the value of x where f(x) has a horizontal…

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Q: Consider the following. u = (-5, 5, 4) v = (0, 1, 6) Find u x v.

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Q: Find the focus, directrix, focal diameter, vertex and axis of symmetry for the parabola -21.2y = x²…

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Q: -5 -4 3 2 4 3 2 1 -2 -3 -4 1 on Use the graph of f(x) above to estimate the value of f'(0) to one…

A: Given: A graph of a function is given as follows:To find: We have to estimate  from the given graph.…

Q: The derivative F' (t) is graphed in the figure below. Given that F (0) = 12, calculate F(t) fort =…

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Q: Suppose that for each i such that 1 ≤ i ≤ N one has [{ What is if N = 69? - f(t)dt = i N f(t)dt

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Q: 77. y = cos.x, y = - sinx, x = 0, x = 1/

A: y=cos⁡x,y=−sin⁡x,x=0,x=π2

Q: Given g(x) 4 2-4' g(-2+h)-g(-2) h evaluate and simplify:

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Q: Select EACH limit that is a term used to evaluate the improper integral below. [ -5 0 dx (x + 4)²·…

A: To find: select each limit that is a term used to evaluate the improper integral

Q: Some say I csc(x) dx = Ln|csc(x) – cot(x)| + C, while other say that [csc(x) dx = -Ln|csc(x) +…

A: The given integral is

Q: 3a If f(x) is continuous and fa f(x)dx = 161.4, what is Sºf Round your answer to two decimal places.…

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Q: Evaluate the integral. 1 4-x 5-x-y SS S 0 0 0 dz dy dx

A: First we integrate w.r.t 'z' followed by 'y' then 'x' as the order of the integral is dzdydx.

Q: If∫−15−97f(x)dx=15and ∫−15−97g(x)dx=11and ∫−15−97h(x)dx=25what does the following integral…

A: The objective of the question is to find the value of the integral ∫ from -15 to -97 of [5f(x) +…

Q: 4. Find the volume of the solid obtained by rotating the region bounded by the graphs of: a. y=x²-9,…

A: y=16-x,y=3x+12,x=-1

Q: dy Find the particular solution to the differential equation 5 - y²sec(x) dx = 0, satisfying the…

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Q: Let y = f(x) be a twice-differentiable function such that f(-1)=5 and dy=(xy² + 4y)². What is the…

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Q: dy Use implicit differentiation to determine given the equation xy + x¹ = e. dx dy dx =

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Q: Using Ratio Test find whether the series is convergent or divergent: √√3 n=1 n 4" n!

A: By using Ratio Test to find whether the following series is convergent or divergent.

Q: 2+3x+4 12. Evaluate [² 2+x+3 ++ dydz.

A: I=∫13∫x2+x+3x2+3x+4ex2+x+44dydxUsing the Power Rule∫xndx=xn+1n+1+C

Q: Let f be a differentiable function such that f f(x) sec² x dx = f(x) tan x-f3x² tan x dx . Which of…

A: Consider

Q: 3. a) a 17 (mod 29) Find the integer a such that and-14 ≤a ≤ 14. b) a 24(mod 31) and -15 ≤ a ≤ 15.

A: (a) (b)

Q: A particle moves along a line with a velocity v(t) - = 2t² + 3t +8, measured in meters per second.…

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Q: If A = (11) 01 " then eat = et tet et (& 0

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Q: Evaluate the indefinite integral. (Remember to use absolute values where appropriate. Use C for the…

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Q: You've been asked to calculate the mass of a conical pile of sawdust measuring 8 meters high with a…

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Q: The population of a slowly growing bacterial colony after t hours is given by p(t) = 5t² + 20t +…

A: The population of a slowly growing bacterial colony after t hour is given byFind the rate of growth…

Q: Select the integral equation that represents the shaded area in terms of f(x) and g(x). O °*If(x) —…

A: Solution is following in explanation step.

Q: A company manufactures 2 models of MP3 players. Let x represent the number (in millions) of the…

A: Given:We are required to find:

Q: Consider the following acceleration a = a=9.8, v(0)=-11, s(0)=0 d's d1² initial velocity, and…

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Q: An angle is between 90° and 180°. You also know that csc = 1.5. Calculate all the other…

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Q: Find and classify the critical points of (x² - 6x) (y² – 7y) 2= Local maximums: Local minimums:…

A: z=(x2-7y)

Q: Use Pascal's Triangle to expand (4x² + 1)¹. Express your answer in simplest form.

A: The given expression .The aim is to expand the expression using Pascal's triangle.

Q: 7. The graph of y = √16-x² has the following transformation applied to it. Determine an equation for…

A: The graph of  has the following transformation applied to it. To determine an equation for the new…

Q: Let f(x, y) = √√x+y Which of the following regions are in the domain of f?

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Q: A baseball team plays in he stadium that holds 68000 spectators. With the ticket price at $9 the…

A: We have given that stadium holds 68000 spectators.When the ticket price at $9 the average attendance…

Q: 5. An object moves along a coordinate line with velocity v(t) = 6t² - 6 units per second. Its…

A: We have to use the basic concept of definite integration.

Q: O Write an equation for the hyperbola OX.H -1

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Q: Identify the definite integral that computes the volume of the solid generated by revolving the…

A: Region is bounded by y=x3 and the line y=x, between x=0 and x=1Rotating the region about y-axis

Q: Use integration by parts to evaluate the integral: [4 4re'dr =

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Q: Given: (x is number of items) Demand function: d(x) = 500 -0.5x Supply function: s(x) = 0.3x Find…

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Q: A particle moves on the circle x² + y² = 100 in the xy-plane for time t > 0. At the time when the…

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Q: A circle has an initial radius of 50 ft when the radius begins decreasing at the rate of 5 ft/min.…

A: Initial radius=50 ftRate of change=5ft/minFinal radius=23 ftThe formula of area of cicle is given…

Q: Evaluate the indefinite Integral, (Use C for the constant of integration.) [ 0² (3+70² 7693/2 dr

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Q: 231 Evaluate the integral (x²yz + xy²z + xyz²)dzdydx 010

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