1. Evaluate the following and give the exact value: -π/2 сosy π-y π/6 sin(y+z) dz dx dy

Q: Find an expression for a cubic function f if f(2) = 80 and f(−6) = f(0) = f(3) = 0. A cubic…

A: given information: a=-5, and the factors of f(x) are x, (x+6) and (x-3) hence, f(x)=a(x)(x+6)(x-3).

Q: [x) = √x. (a) Simplify f(22 + h) − f(22) - h Algebraically simplify your answer until you have…

A: Given query is to find derivative using definition and then equation of the tangent.

Q: Q15b. Define the sets A, B, C, and D as follows: A = {y ∈ Z : 2 < y ≤ 9 and y is odd}. B = {1, 4, 6}…

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Q: Assume that (x,y)=(t,1+t) is a solution to the system: ax+by=1 cx+dy=2 Show that for all…

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Q: Q26 Sasha is trying to bound the error of her M10 approximation of S f"(0) = 0 and f"(T) = 0 and so…

A: We have to find part a,b and c .

Q: y-1/10(e^(5x)+e^(-5x)), for x:[-4,4], about the x axis. Find surface area

A: Let's find surface area.

Q: 4.y=x y-y y+1 y(3)=-1

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Q: The temperature is modeled by the linear function T = 0.03t+ 7.50, where t represents the years…

A: Here is the solution:

Q: Evaluate the multiple integral 2x [ [² r dz dy dr Do not include spaces.

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Q: Determine whether the given differential equation is linear or nonlinear, and give its order.…

A: In this question, we need to check whether the given differential equation is linear or non-linear…

Q: Sketch a possible graph of a quadratic function which has two real roots (one positive, one…

A: Here, suppose the quadratic equation is: y=px2+qx+c Given that it passes through (0,-4).

Q: In a certain sci-fi apocalyptic movie set in the year 3020, the narrator said the maximum acceptable…

A: Given: In year 3020, Rate of decay of atoms of Uue is proportional to the amount present. After 10…

Q: Eliminate the constant: 3x 3x y=c₁₂e³+€₁₂€ ³ Oy"-4y+3y=0 Oy"-6y¹+9y=x Oy"+ 6y' +9y=0 Oy"-6y'+9y=0

A: Given: From the above, we see that the root of the characteristic equation will be 3, 3. So, the…

Q: 3. Evaluate f'(5) for y= √4x + 5

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Q: Use Convolution to solve inverse function: पूर्ण होजा? solve inverse laplace of a

A: Find the Laplace Inverse of a function using convolution L-11s3s-1=?

Q: A person’s life expectancy can be modeled by the function g(x) = 10.761ln(x + 1) + 27.98, where g(x)…

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Q: 10. Find the values of x where the tangent line is horizontal. f(x) = (x² - 9)²

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Q: Eliminate the constant: y=c₁e²+c 3x ad Oy"+y'-6y=0 Oy" + 5y'+6y=0 Oy"-5y¹+6y=0 Oy"-y'-6y=0

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Q: (x-p)(x-q)² (x-r) If p, q, and r are real numbers that may or may not be equal, the graph of the…

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Q: (1 t) Let A = (2, -3) and B = (-3, 3) be points in R², and let C = (4,-4, 4) and D= (2, -3,-1) be…

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Q: (1) Let a = and b =. Show that there are scalars s and t so that sa + tb =. You might want to sketch…

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Q: The equation of a rational function is given below. f(x) =   +1   Which statement describes the end…

A: Topic:- function

Q: . Use congruences to show that there is no solution to x³ + x² − x + 1 = 1522745.

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Q: IF Find А II = 2 1 0 -1 -2 3 4 -5 C = 1- 3At + 2B - AC 2-|Adj A| OR |Adj B| 325 4 3 0 -2 5 -2 4 -5 2…

A: Let's solve given matrix problem.

Q: 9. -1 et - ex -2x e²x + e +2 dx =

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Q: Determine the value of k such that y=4x²-3e2x is a solution to x (1− x) y''+ (2x² - 1) y'+k(2x - 1)…

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Q: Problem 1: Using differentials, approximate the change, in terms of 7, in the total surface area of…

A: Use diffential concept

Q: 3. Determine whether the following function y = c₂x + c₂x³ + 2x²e² is a solution to the differential…

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Q: Create 3 non-exact differential equations and solve for their test for exactness and show complete…

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Q: 6. g(x) = sec (3x²)

A: We can solve it by chain rule dy/dx = dy/du * du/dx

Q: Vy² + 2 y+x5y-6 3. Find the limit: lim

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Q: Identify whether the limits of the following does exist or not. If yes, find the limit and if not,…

A: Given function  for x = 2.90 f(2.90) = same way find values for other points

Q: raphs of the functions f and g are given. y 1 -f- 9 XV X

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Q: 2. Find the equation y=x²-3x² of the normal line at a given point on the given curve. + 4 @ (2,8)

A: Solution: y= x4 -3x2 + 4  @ (2,8) dydx=4x3 - 6x  at x =2=32-12=20

Q: 8. If c and n> 0 are integers, evaluate the following limits or explain why they do not exist (DNE).…

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Q: 1. 2. Find the following limits, if they exist. (If a limit does not exist, enter DNE.) 3. 4. f(x) =…

A: Here we have to find the limit of the function.

Q: 2. y' = 2y4+x4

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Q: rcos y 慮 S Sỹ¯³ sin(y+z) dzdxdy

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Q: Q2: Construct the difference table from the following data. x y 0 1 1 4 2 21 and then find y" (3.2),…

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Q: 14) I am going to invest my money into two different accounts. The first account gives 4% interest.…

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Q: 16 = dx / x7 3/5+4x⁹

A: This question has been solved without using trigonometric substitution

Q: Evaluate lim 4-2 1 [-x] 1 |x|

A: To evaluate the following limit.limx→-2+ 1-x-1x

Q: lim =√x² - 2x + 5 X→-2 lim x→2 (5(x² − 1)² – 10)

A: To find out the limits

Q: 7. f(x)= = x² cos²x sinx

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Q: 23 لا تلاح da

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Q: Determine the value of k such that y=(1-sinx) * is a solution to 2y'=y³cosr

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Q: xy"-7xy+ 15y = 0

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Q: Using differentials, approximate the change, in terms of pi, in the total surface area of a closed…

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Q: A=70(1.06)t what is the rate in percentage

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Q: Using disks or washers, find the volume of the solid obtained by rotating the region bounded by the…

A: Topic = Volume