Find the slope and y-intercept of the line through the point (6,7) that cuts off the least area from the first quadrant. slope %3D y-intercept =

Q: 1. Sketch the region enclosed by the given curves: y = e*, y = x² – 1, x = –1, x = 1. Find the area…

A: (1)

Q: H.w dy ーレ dy Xy in

A: Since you have posted multiple questions with sub parts, as per our guidelines , we will answer the…

Q: Find the absolute maximum and absolute minimum of 9(t) = t/4– t on the interval [0.8, 2.8]. Enter…

A: topic - application of derivatives

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Q: If an object's position over time is given by the function d(t) = (t +3)e i for t > 0, on what…

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Q: Find the following Laplace and Inverse Laplace Transform of the function. 5. f(t) = e-4t (t-cos(t))

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Q: Consider the curve segments: $1: yx from xto x= 3 and $2: y = Vi trom x to x= 9. Set up integrals…

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Q: Determine (4x³ + 3x2 + 5) from the first principle when x = 2 Determine the differential coefficient…

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Q: Find the particular antiderivative of the following derivative that satisfies the given condition.…

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Q: Evaluate the iterated integral. NOTE: Enter the exact answer. S r xy dy dx dz 0,

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Q: 5. y = (x? - 4) / (x² - 2x)

A: The given function,   y=x2-4x2-2x

Q: evaluate lim f (x) and lim f(x). X--00 -5 + 2e-* f(x) = %3D 5e-+6

A: f(x)=-5+2e-x5e-x+6limx→∞f(x)=limx→∞-5+2e-x5e-x+6             =limx→∞-5+2ex5ex+6…

Q: Determine whether the sequence converges or diverges. If it converges, find the limit. (If the…

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Q: At least one of the answers above is NOT correct. Suppose f(x) is continuous on [3, 7] and -2 <…

A: Solved below

Q: An open box is to be made from a square piece of material, 38 inches on a side, by cutting equal…

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Q: Find the distance between the point and the plane. (Round your answer to three decimal places.) (1,…

A: Distance from a point  (x0,y0,z0)  to the plane ax+by+cz+d=0 is given by    ax0+by0+cz0+da2+b2+c2…

Q: 3 Find the arc length of the astroid: x = cos t, y = sinº t, 0 <t < 2T

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Q: What would be the shape of the graphr= 2 cos 0, given that 0 = 0, 7, 5, ? semi-circle in the first…

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Q: A solid right cylindrical cement block of volume 97 ft³ is to be made, and then painted except for…

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Q: ng the shore and 60 meters from the sh mps into the water and swims from the second and swim at a…

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Q: Find the arc length of the parametric curve. x = 3 cos(t), y = 3 sin(t), z = 4t; 0 <t<+ %3D %3D

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Q: Convert the Cartesian coordinates (1, 0) to polar coordinates. (1, 0°) (1, 90°) (0, 0°)

A: The cartesian coordinate is  x, y = 1, 0 To evaluate: The polar coordinate corresponding to the…

Q: Let C be the parametric curve defined by x(t) = t² – t – 2, 1 y(t) = t3 – t2. 2 %3D (-:) 3 -2,…

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Q: The absolute max occurs att The absolute min occurs at t

A: Follow the procedure given below.

Q: Determine the points at which the limacon defined by the polar equation r= 3 +2 sin e Has horizontal…

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Q: Find the limit. lim tanh(x)

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Q: A function f(z) and interval (a, b) are given. Check if the Mean Value Theorem can be applied to ƒ…

A: Given query is verify the mean value theorem.

Q: Choose the graph of y= 2 arcsin x, - T S YS T 27

A: when x=0, y=0 at x=1 then y=π at x=-1 ; y=-π

Q: Find the particular solution of the differential equation. dy 7 - 7x° e -×' ; y(0) = 4 dx y =

A: See below the answer and calculation

Q: の Cm (1av)ー lim XDO

A: lim   ((1+x)3/2 -1)/x x  -- 0 here 0/0 for so we use la hospital rule and differentiate above and…

Q: Find the general indefinite integral. 8v(v? + 9)? dv Step 1 We'll begin by expanding (v + 9)? = 18…

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Q: Find the general or particular solution, as indicated, for the following differential equation. dy -…

A: dydx=-0.4 ydyy=-0.4 dxvariable separable;∫ dyy=-0.4∫ dxln y =-0.4 x + ln cy=c e-0.4 x

Q: (9) If sin(A) = /2, sin(B) = - ½, "/½ < A < r, and n < B < 3*/2, find cos(A + B) (A) 0 (B) /2 (С) —…

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Q: True or False, If f' (3) = f" (3) = 0. then I 3 MUST be an inflection point. (Remember = to give…

A: It is given that, f'(3)=f''(3)=0 then x = 3 must be an inflection point.

Q: f(x) = 7 - 18x + 3x2, [2, 4]

A: We are asked to verify the Rolls theorem.

Q: Whale and Kanmuro are two islands located in the Chimera archipelago. These two are separated by a…

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Q: The marginal average cost of producing x digital sports watches is given by the function C'(x),…

A: NOTE: Refresh your page if you can't see any equations. . the marginal average cost function is…

Q: [43 80 -60 Let A = Find an invertible matrix X and a diagonal matrix D such that [30 60 -42] D =…

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Q: The figure shows the graphs of the cost and revenue functions of a company that manufactures and…

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Q: 7. Determine the magnitude and (-2,–1) and a terminal point o

A: Given query is to find the magnitude and the direction angle.

Q: Express the polar coordinates (-2, -7) as Cartesian coordinates. (2, 0) (0, -2) O (0, 2)

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Q: If a function f is differentiable on [7,11], then which of the following statements must be true?…

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Q: x2 V1-x2 dx Use trigonometric substitution

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Q: tan ³x sec4x dx. Use trigonometric group

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Q: Find the solution of the following differential equation. Take the constant of integration to be…

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Q: Given curves 7(t) (5t, 3t, 5t 5) and ü(t) = (3t°, 2, 4t + 6t) find the derivative of the cross…

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Q: nsider the equation below. (If an answer does not exist, enter DNE.) f(x) = x3 – 6x2 – 15x + 3 (a)…

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Q: Use the graphs of f and g, shown below, to find the following. yA 4. ((2). If the derivative does…

A: Write the derivative of the form u/v then substitute the value of x at which we have to find the…

Q: 11.) Find the area inside r -3cos(e) and outside r = 1+ cos(e)

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Q: dx is solved by trigonometric substitution, which of the following substitutions is used? x2- 2x – 4…

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