Determine the set of x-values where f(x) = 8x² + x - 8 is continuous, using interval notation.

Q: What is the general solution to the the differential equation3y" - y'- 2y = 10e *?

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Q: 2. The population of a city is growing continuously by the same percent each year. The population at…

A: We can solve this by following methods.

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Q: valuate: fe²z cos(e³)dz = + C Hint: Rewrite e² = e.e²

A: Please refer to the image below

Q: 7. A traditional first experiment in a physics laboratory is to make 98 observations ab records the…

A: Given formula for linear regression is as below  take t as x and h as y. find mean value

Q: Find a vector parametric equation (t) for the line through the points P = (1, −4) and Q = (−2, −9).

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Q: A function is given below. Determine the average rate of change of the function between t = 2…

A: Given function, f(t)=7t   from t=2  to t=2+h

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A: Find the equation for the tangent line to the curve at the given point by using the limit definition…

Q: 6. (01.03 HC) Values of f(x) at selected values of x are shown in the table. X 2.75 2.9 2.99 3.01…

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Q: Find ||u₁y|| if u = (2,5), v = (8,2). # 5 -X (Express numbers in exact form. Use symbolic notation…

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Q: Find the distance of the point (4, 2, −4) from the line r(t) = (−1+ 2t, 1+ 2t, 7 – 3t). Answer:

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Q: 3. f(x)=-2[x]

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Q: [1 2 3] Find A-¹ if A=4 1 5 L6 0 21

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Q: Find the Average Rate of Change of the following function over the interval [2, 5] (That is, from t…

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Q: Let f and g be functions defined as f(x)=x²- 2x + 4 and 25 4 DNE 1 g(x) = 3x² + ²3. If h(x) ≥ g(x)…

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Q: 7. y=x+²³² +1.

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Q: If f(x) = 7 and g(x) 4x + 3 (fog)(1): (gof)(1) = = √√45x + 4, compute the compositions (fog)(1) and…

A: Given , f(x)= 7 / (4x+3) And g(x)=√(45x+4)

Q: Find the set of all solutions of each of the following differential equations.  y" =32.

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Q: 4.y = C₁e-2x + C₂e³x

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Q: Calculate the cross product assuming that = (-2, -8, -2) u x w = (4u − w) × w = (100)

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Q: O V(2)-V(1) 1 O V(lim t) t-1 The size of a balloon is changing with respect to time, such that the…

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Q: The real number t corresponds to the point P P(-3,-4) on fraction, if necessary. on the unit circle.…

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Q: Write an equation of the plane with normal vector n (7,5, −4) passing through the point (1, −5, 1)…

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Q: Let f(x) = 4x - 9. Simplify each of the following expressions. f(a)= 4a - 9 f(a+h) = 4a +4h-9…

A: Given query is to perform indicated operation on th function.

Q: Given the function f(x), find f'(x) f(x) = 9x² COS X

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Q: Find the equation of a plane that is perpendicular to the vector 4 i + 2 j - 2 k and passing through…

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Q: K For the piecewise function, find the values h(-9), h(1), h(S), and h(7) -5x-9, for x<-3 H() = 5,…

A: Topic - Functions

Q: Find lim x→-3 sin(−4 π x)   lim x→-3 sin(−4 π x)

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Q: 1. f(x) = (x+4)² 2. f(x)=√x +3 +40 CHI

A: 1. Parent fuction will bef(x) =xto understand better I have drawn the graph using online tool (will…

Q: 1. Prove that for all x, y ER, max (x, y) x+y+lx-yl 2 x+y-lx-yl 2 and min (x, y)=-

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Q: 5. I Find the area of the region enclosed by the curves y = 3x³ - x²-10x and y=2x-x². (x ≥ 0) (a)…

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Q: Find a formula for the nth term of the sequence in terms of n. 3² 3³ 34 1 3 3 - 4' 6 8 " 10 " 12

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Q: {(1.-).(2-3) (0,5), (1.3),(4,5), (-1,5),(4-4) 6. § (3,-2). (-8.-7), (0,6).(-3,4),(6-³3).(-1,6),…

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Q: lim t→l 1+√t+ √t+√t t² + 1 + 1 t³-2

A: I have solved step by step in detail...and I have written answer up to simplified…

Q: Evaluate the following integral. 6 x (x² + 5)² dx Find the partial fraction decomposition of the…

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Q: f(x)=(x-6)³+4, [4,7],f(c)=3 3

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Q: se the isosceles right triangle and the 30°-60°-90° triangle to complete 45 r √2 - 45 60⁰ 30% √3

A: Part 1 :  For triangle                  For θ=30° It is right-angled triangle.…

Q: 43. YA 3 -1 y=2x L (3, 3) 3x

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Q: C. Find the standard form of the equation of a circle given the following conditions. 12. Center at…

A: Given  Center of circle h, k=2, m point on the circle is 0, 1 Radius is equal to twice of the…

Q: 10- x - x² if 3x + 13 if In(x-1)-2 if Calculate the following limits. Enter "DNE" if the limit does…

A: Topic - limits and functions

Q: Make a table of values for the equation. y = 5x X -2 1 1 2 || y Sketch a graph of the equation.

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Q: Express the following functions in the form u+iv • f(z) = \n (1+z) P

A: Given function is: f(z)=ln(1+z) Let z=x+iy

Q: Find the projection u||vy = (x, y) of u = (6, -7) along v = (1,2). (Use symbolic notation and…

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Q: Find the value of a, b, c, and d. Enter all answers in exact, reduced form. No decimals are allowed.…

A: Please refer to the image below

Q: C. Find the standard form of the equation of a circle given the following conditions. 12. Center at…

A: Find the equation of the circle whose centre is at (2,m), radius is twice the y co ordinate of the…

Q: Use the given conditions to write an equation in point slope form and slope intercept form. 8. Slope…

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Q: C. Find the standard form of the equation of a circle given the following conditions. 11. Radius is…

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Q: 2) A construction company uses the function S(t) = 28,000 - 2000t to determine the salvage value…

A: 0

Q: B] Find the domains of the following relations. Write them in interval notation. 1) f(x)=√x-9 2)…

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Q: average

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