15-16 Find the domain of each function. 1 - et² 15. (a) f(x) (b) f(x

Q: Find the solution of each of the following initial value problems. y(0) = 1 (a) y'-y = 2te²t, (b) y'…

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Q: It takes 15 min longer for John to wash clothes compared to his sister. If they work together, it…

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Q: Given f(x, y, z)= xyz, find fxyy

A: Derivate f thrice with respect to x, y and then again with respect to y.

Q: Use Gaussian elimination and Gauss Jordan method to solve the system of linear equation. x - 2y-6z =…

A: The given system of linear equations, x-2y-6z=122x+4y+12z=-17x-4y-12z=22 We have to find the…

Q: 1) Eliminate the constants from the following equations: y = x² + C₁e²x + С₂e³x y' = 2x + 2C₁e²x…

A: NOTE: As per our guidelines, I have solved the first problem. If you want solutions of rest, kindly…

Q: If= 1π sin(0) = use the unit circle to find

A: Please refer to the image below

Q: 3. Calculate the angles that vector H = 3ax + 5ay y-, and z-axes 8az makes with the x-

A: Given Vector -   H = 3ax+5ay-8az since , angle of vector with x-axis =…

Q: An amount of $500 was invested in 1995 and the investment grew as shown in the following table.…

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Q: y" + 4y = sinx

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Q: ty"+ t²y' - (Sint) √ y = t² - t +

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Q: Let U be the universal set of natural numbers less than 11. Consider the following two sets. A = {7,…

A: NOTE: Refresh your page if you can't see any equations. . U be the universal set of natural…

Q: Use the definition of derivative to find f'(x) and f"(x) f(x) = 4x² + 3x + 2 f'(x) =

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Q: In Exercises 5-14, determine the convergence of the given series using the Ratio Test. If the Ratio…

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Q: Suppose that the weekly sales volume y (in thousands of units sold) depends on the price per unit…

A: We have to find the value of derivative at $21 and interpret the answer.

Q: if x ≤ 2 Let f(x) = = if x > 2 If f(x) is a function which is continuous everywhere, then we must…

A: Given function, f(x)=4x-5if x≤2-3x+bif x>2 Here function is continuous everywhere ,

Q: A rectangular piece of land has dimensions 1050 ft by 550 ft. Find the area of the land to be…

A: The length of the rectangular land, l = 1050 ft Width of the land, w = 550 ft To evaluate: The area…

Q: Q2: Use the substitution x² = sing to show that 1 √ √ ² x dx = [] 4√2TE

A: See this solution in below.

Q: The price per barrel of crude oil in the period 1980-2013, in constant 2014 dollars, can be…

A: Topic- functions and derivatives We are given,Price per barrel of crude oil since t years of the…

Q: Find the particular solution of each of the following. y(1+21n²) dx+xdy=0; y(e)-e

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Q: Find f'(a). f'(a) = f(t) = = 8t + 44 t + 7

A: The given function is f(t)=8t+44t+7. We have to find derivative of f(t). Here we use quotient rule…

Q: Consider the cylinder on the right (a) Write an equation expressing the fact that the volume is 221…

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Q: 3)Find a function whose graph is a parabola with vertex (3, 1) and that passes through the point…

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Q: - If f(x) = 4x² – 20x + 21, evaluate_lim_f(8 + h) − f(8) h→0 h If an answer does not exist, enter…

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Q: 1. Circle the function if it is a (a) f(x) = 3x³ - 2x² + x (b) f(x) = 5x ² +5x² (c) f(x) = 2…

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Q: Use the graph of y=f(x) to graph the function g(x) = -f(x)-1. y = f(x) Ay d 2 Choose the correct…

A: y = f(x) g(x) = -f(x) -1 here f(x) graph is given  from that we have to find g(x) graph  here from…

Q: rdp-(p+√√pr)dr=0

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Q: 4

A: Concept: Given: Demand for the education: P=75-Q Supply for the education: P=2Q Due to decrease in…

Q: v = fb an V (x − 3)(x x= y₁²³-4y+3 чуте x = 3 X b 2₁₁ × [ f(x)] dx 29 x= 1x 2 y

A: v=2π∫13y(1+(y-2)2dy v=2π∫13y(1+y2-4y+4)dyv=2π∫13(y+y3-4y2+4y)dy

Q: y(x) = C₁ e ² + C₂ e ²*, + 4 SiN X, Y (0) = 1, y' (0) = -1

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Q: 9. n=1 1

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Q: angle between 0∘0∘ and 360∘360∘ that is coterminal with the 1950∘1950∘ angle is what degrees.

A: Topic:- trigonometry

Q: Solved the following set of equations 16x + 2y 2z = 16 2x 14y + 4z = -8 4x + 2y + 18z = 24 Using…

A: Given: 16x+2y-2z=16 2x-14y+4z=-8 4x+2y+18x=4

Q: Find the area of the region enclosed by the graphs of 1 1 √1-9x²² NOTE: Enter the exact answer. Y…

A: Find the area

Q: 117 log(u) | ²7 = = = log (2) logcos 2 2 2 7. Use Logarithmic Differentiation to compute d Vcos² x(x…

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Q: t costs $90 to rent a car driven 100 miles and $140 for one driven 200 miles. If x is the number of…

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Q: 2. Divide 20 into two parts. Find the two positive numbers if: (a) their product is a maximum; (b)…

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Q: 6.) Find the limit (if it exists). 6x² + 3x + 10x²+x+ lim x+²)

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Q: -5 -4 -3 -2 -1 5 4 3 -4 2- 0 --10 -2- -3- -57 1 2 3 4 5

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Q: T = 7/24 31nx - secydx - 5xsin ydy=0;y (e ³) : .

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Q: Find inverse g(x)=x²-2x, x²1 f(x)= 1+√2+3x S y = (2+ 3√x) ³ 1-√X Y = T+√x

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Q: 5. Determine the domain ONLY 4-x g(x) = /4-x

A: We have to find the domain of g(x)=4-x4-x Remember Domain of f(x) is defined when f(x)≥0 and domain…

Q: Solve (e) (1-x²)y' = 4y; y(0) = 1.

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Q: 8. y = In ln 1+sinx 1–sinx

A: As we know that; The Chain rule: fgx'=f'gx·g'x The Quotient rule: fg'=f'·g-g'·fg2 And the common…

Q: 1. f(x). = X+I

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Q: For the given function f(x), the point c, and a positive number e, find L= lim f(x). Then find a…

A: Let's find value of L.

Q: Q3/ Use the l'Hopital's rule to find the limits 1) lim X-0 sinx-x x3

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Q: Find an equation for the line tangent to the curve y = (√x + 8)(x4 + 3) at x = 1. y =

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Q: 1. A carpenter can construct book cases at a cost of P400 each. If the carpenter sells the book…

A: Given:- Carpenter sells the book cases for x pesos each And 300-2x book cases will be sold per month…

Q: Check whether each differential equation has the indicated solution. Determine which solutions are…

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Q: Given f(x, y, z) = xyz, find fyyx

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