The shaded region between the graphs of y=-2x² + 20 and y = 3x - 15 is displayed below in orange. 25 -6 x

Q: Question-1: Prove that 1-cos(x) lim 0 Hint: Use the conjugate of 1- cos(x). 20 is zero using that…

A: Here we have to find the limit.

Q: 16-25 x² dx

A: Given,             ∫16-25x2dx

Q: ƒ(x) = x² +1, (0;2π), T = 2π.

A: We have to find fourier series by the cosine f(x)=x2+1 in [0,2π]

Q: Consider the mixing process shown in the figure. A mixing chamber initially contains 4 liters of a…

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Q: Let f(x) = x³ – 6x +3. Compute ƒ'(1) using the limit definition. ƒ'(1) Find the equation of the…

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Q: Guess the value of the limit (if it exists) by evaluating the function at the given numbers. x² + 2x…

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Q: 2. Verify that each quotient is indeterminate, and then evaluate the given limit. 1-x² 1 a. lim x→1…

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Q: Find the vector parametrization r(t) of the line L that passes through the points (4, 1, 4) and (7,…

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Q: 2. Subtract f(x) from f(x+h).

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Q: Consider the following systems of linear equations. 2x + 5y2z = 14 x + 3y - 4z = 5 x + 2y + 2z = 9…

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Q: in solving the problem. Directions: Find the dy/dx by implicit differentiation. X^2 + y^2 = 100 X^3…

A: We can solve the given problem by using the implicit differentiation

Q: A pet supply company has surveyed 887 of its customers to determine the types of pets that its…

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Q: as x 1 Let #E(³ (R), such that ‡ (x) = 2(x-1) + 3 (x-1)³ + 0((x-1)³) It's true that A. (2) = 5 B. ¹¹…

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Q: -6 (18 x x 4 + ²) bx² Y ។ 'F' 8.

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Q: The base of a sc x² + y² = 16. x² + y² = 16 → x oss-sections perpendicular to the x-axis are eq…

A: We are asked to find the volume of the given solid.

Q: iii) Find the value of t when f'(t) = 25. iv) Let g(t) = tf(t). Find g(t), then find the derivative…

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Q: Find the distance from the point s (−4,1,2) to the line x=9t​, y=4t​, and z=4t.  The distance is d =…

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Q: y = C₁ e²^ + C₂ e²^ + Cze=²

A: To make a differential equation after eliminating the arbitrary constants. y=c1e-x+c2e2x+c3e-3x

Q: Let f(x) = 3 + 2(x-3) + 0(x-3), as x→3 and let g(x) 2 B. g (3) = ² 3 ·g is defined and…

A: We will find the required.

Q: Initially 10 grams of salt are dissolved into 30 liters of water. Brine with concentration of salt 3…

A: Given: Initially 10 grams of salt are dissolved into 30 liters of water. Brine with concentration of…

Q: 7sin(In(x)) d x

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Q: a.) find x intercepts and y intercepts b.) odd or even multiplicities? c.) find power function d.)…

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Q: Find the general equation of the differential equation: (a)  (y-cos²x)dx + cosxdy = 0

A: To find the general equation of the following differential equation. y-cos2 x dx+cos x dy=0

Q: Find the indefinite integral. (Use C for the constant of integration. Remember to use absolute…

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Q: A rich uncle wants to make you a millionaire. How much money must he deposit in a trust fund paying…

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Q: Solve for the following equations each with a specified method: Using Elimination: 1. 5x + 3y = 10…

A: Given system of equations:- 5x+3y=10 ...........................................(1) 10x+6y=0…

Q: [4³6 4x e¹4x dx =

A: We have to find the integral.

Q: Find an equation of the circle passing through the points  (−2, 3), (−5, 6), and (1, 2).

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Q: Find the vector equation for the line of intersection of the planes 2x + y - 5z = 5 and 2x + 2z = -1…

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Q: Find the distance between the point and the line given by the set of parametric equations. (Round…

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Q: Let F (x, y) = 8Q A. Compute 82 yi+zj z² + y² and let C be the circle r(t) = (cost)i + (sin t) j. 0…

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Q: Apply the Laplace operator to the function h(x, y, z) = ef sin(-6y). V2h

A: h(x,y,z)=e7xsin(-6y)we  know  ∂xn∂x=nxn-1∂ ∂x(ex)=ex∂(sinx)∂x=cosx…

Q: Find a general solution to y" + 36y = 12 sec (6t). Use a and b for the constants of integration…

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Q: 6. What is the slope of the line y = -7? 7. What is the slope and y-intercept of the line of the…

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Q: tan (sin-)

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Q: 2. Find the area of the regions enclosed by the parabolas y = x and y = 2x − x²

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Q: If dy = (2x - 3) dx and y = 2 when x = 3, find the value of y when x=5. Ans. y = 12

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Q: 1 Complete the computations JC-21, 23) - (2,6)= (-25,2). 2.) 3(133,-0.30) + (-399, 0.99,0) = (?.?.?)…

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Q: Find a power series expansion for f'(x) given the expansion for f(x). f(x) = Σ Try-5 7-8 6=5 f(x) =…

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Q: Evaluating an Arithmetic Combination of Functions In Exercises 19-32, evaluate the indicated…

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Q: 6x +29x5 x² + 8x + 15 identify any horizontal or vertical asymptote as well as any removable…

A: The given function is fx=6x2+29x-5x2+8x+15. We have to find the vertical, horizontal asymptotes and…

Q: 1. a. Write a set of ordered pair that defines the relation given in the graph. -0 b. Write the…

A: We see all values from given graph .

Q: . Find the shortest distance between the: x−1_y−3 a. point (1, 3, 2) and the line *-¹-y-3_2–7 1 -1 2…

A: Given planes:- P1: x+2y-5z-10=0 P2: 2x+4y-10z-17=0

Q: Complete the trinomial so that it is a perfect square. Then factor the trinomial. m2+22m.  Find the…

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Q: 5. Use the graph of y = f(x) to answer the following. a. f(-2) = -5-4-3-2-1 43 2 S - Ņ w y = f(x) 1…

A: The domain of a function is set of values that we allowed to put in our function.and Range of a…

Q: Find the equation for the plane through Po(-4,-3,8) perpendicular to the following line. x= -4+t,…

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Q: When a deposit of $1000 is made into an account paying 4% interest, compounded annually, the…

A: Given :   Formula for average rate of change :

Q: For wages less than the maximum taxable wage base, Social Security contributions (including those…

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Q: 4 - 4 cos (60) 0 0 0 tan (60) 3. Find lim

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Q: 1. The graphs of y = f(x) and y = g(x) are shown below. Determine lim (f(x) + g(x)) and lim (f(x) ·…

A: We will compare both graph