(a) Define the following hyperbolic functions directly in terms of the exponential function (i) sinh. (ii) cosh. (iii) tanh. (iv) cosech. (v) sech. (vi) coth.

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Q: 43. Find f (0) for the function below. f(x)=sin²(3-x) -2 sin 3 cos 3 -2 cos 3 6 sin 3 cos 3 6 cos 3…

A: f(x)=sin23-x

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A: We have to find the function.

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A: NOTE: Refresh your page if you can't see any equations. . here initial velocity is zero so take v0=0…

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Q: 40. Ten thousand raffle tickets are sold at $2 each for a local library benefit. Prizes are awarded…

A: We need to find expected value.

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Q: 1. Solve the initial value problem y' -1 -2 1 4 2 5 2 -2 0 y, y (0) E 5 -1

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Q: (a) The Cartesian coordinates of a point are (1, 1). (i) Find polar coordinates (r, 0) of the point,…

A: we need to find the polar coordinates

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Q: Find at least 10 partial sums of the series. (Round your answers to five decimal places.) n 1 2 3 4…

A: Sum of GP

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A: Topic = Area

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Q: How many of the following statements is/are true? In(xy) = (lnx) (In y) • The slope of a line…

A: To determine the number of statements that is/are true.1 lnxy=ln xln y2 The slope of a line tangent…

Q: At what point (x, y) is the function f(x) = 8x - 3 closest to the point (3, -6)? Enter an exact…

A: To determine the point x, y on the function fx=8x-3 is closest to the point 3, -6.

Q: he manager of a large apartment complex knows from experience that 110 units will be occupied if the…

A: NOTE: Refresh your page if you can't see any equations. . x=number of units y=price per unit from…

Q: X A dx dt X 1: State the Pythagorean theorem for this problem as function of x,y and the der 29…

A: Topic:- application of derivatives Note:- as per our guideline if more than three subparts posted…

Q: 5 5 it ff(2) dx = -3. [ * f(2) If 1. [² f(x) dx = = [ 5 2. [*[19(x) + 4] dz : = 5 | [₂9(x) dx = ² ·*…

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Q: Maximize the function f(x,y,z) = x² + 2y − z² subject to the constraints 2x - y = 0 and y + z = 0.…

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Q: 1. Describe and sketch the following set of points defined by the following conditions. (1290221 and…

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Q: A company manufactures and sells x television sets per month. The monthly cost and price-demand…

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Q: 7. fx² sinxdx 9.f x² Inxdx

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Q: Find the derivative of the function at Po in the direction of A. f(x,y,z) = -5ex cos (yz),…

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Q: 1. Find the most general antiderivative or indefinite integral for the function. (Ilint: Using a…

A: to find integration.

Q: Compute the curvature of the curve x=2y^2-3y at (4,2).

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Q: Find the second derivative of the function. (Factor your answer completely.) f(t) = t^(2)e^-9t f ''…

A: Find the second derivative of the function.  f(t)= t2e-9t

Q: . antiderivative X-1ady toss dx x²

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Q: 1) a) Solve the following inequalities: (i) 5 (11-q) <q +49 10m +2<8-5m 3 (iii) x² ≥ 15 - 2x (ii) 7m…

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Q: Find the length of the arc of the curve from point P to point Q. y = 1x², p(-1, ¹), Q(¹, 1) || Need…

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Q: Find equations of the tangent line and the normal line to the graph of the given function at the…

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Q: Use the Mean Value Theorem and find all points 0<c<2 such that ƒ(2) —ƒ (0) =ƒ'(c) · (2-0) : ƒ(x) =…

A: See this solution in below.

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Q: 0 3 1+1x² dx

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Q: The given curve is rotated about the y-axis. Find the area of the resulting surface. y = √√x, 1 ≤ y…

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Q: Consider two nonnegative numbers x and y where x + y = 2. What is the maximum value of 11x²y? Enter…

A: Let's find maximum value of function.

Q: Consider the following. 8 [²x³ dx r8 Rewrite the integral ¹11° (x x³ dx = 1,020, • 8 8 8 0 [*(x -…

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Q: Out of all the techniques of integration (by parts, partial fractions, trigonometric) which one do…

A: Use the basic principle of integration by parts.

Q: All the real zeros of the given polynomial are integers. Find the zeros. (Enter your answers as a…

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Q: Try again Practice similar r answer is incorrect. 2 attempts remaining. the equation of the tangent…

A: We have to find the equation of the tangent plane from the given information

Q: Find the indefinite integral. (Use C for the constant of integration.)     8x(4x2 + 3)6 dx

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Q: The vertical velocity of a cork bobbing up and down on the waves in the sea is shown below. In this…

A: The Solution is given below:

Q: Find. lim X-0 2-2cosx X

A: use the l hospital rule for finding the limit.

Q: Draw and label diagram to help solve the related-rates problem. The radius of a sphere decreases at…

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