Find the equation of the line tangent to the graph of f(x) = (In x)² at x = 5. *** y=0 (Type your answer in slope-intercept form. Do not round until the final answer. Then round to two de

Q: Find the critical point and the interval on which the given function is increasing or decreasing,…

A: dxndx=nxn-1f(x)=5x2+4for critical points put f'(x)=0

Q: Compute the Taylor series of the function around x = 1. f(x) = e7x f(x) =

A: Compute the Taylor series of the function around x = 1. f(x) = e7x

Q: a) log (x² - 1) - log (x − 1) = 1 b) log4x x = 2

A: Given query is to find the value of x.

Q: A cone-shaped pile of sawdust has a base diameter of 24 feet, and is 7 feet tall. Find the volume of…

A: Find the volume

Q: Find the complete solution of the linear system, or show that it is inconsistent. (If the system has…

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Q: 3. Find parametric equations for the graph of a circle centered at (-3,1) and radius 3.

A: Let's find parametric equations for the graph.

Q: 2) Solve for x : a) e* = 80 b) 3¹-* = 9²x g2x

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Q: ďy dx² If xy + 2 = -x then find y at the point (1, -3) in simplest form.

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Q: An airplane flies due east from point A to point B, a distance of 200 miles. The plane n turns on a…

A: Given query is to find the distance between A and C.

Q: Suppose that x and y are related by the equation 5x² - y² =4 and use implicit differentiation to…

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Q: Convert the equation to polar form. (Use variables r and as needed.) x = y

A: To convert the equation in polar form. x=y

Q: Evaluate. 2 0 √2x dx

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Q: Determine the slope of the tangent to the curve y = x^2 - x at the point with x -coordinate 4. Show…

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Q: A projectile is launched straight up in the air. Its height (in feet) t seconds after launch is…

A: Let's find average height.

Q: Consider the parametric equations x = (t + 1)² and y = t + 2 for-3 St≤ 3. (a) Make a brief table of…

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Q: Determine whether the Mean Value Theorem can be applied to f on the closed interval [a, b]. (Select…

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Q: Of all students at the University of Metropolis, the proportions taking certain numbers of units are…

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Q: Use the properties of limits to compute the following limit exactly lim [(x-3)³ (5x+1)²]

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Q: Match each of the Maclaurin series with the function it represents. x²n+1 (2n + 1)! A. arctan(2) B.…

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Q: A company determines that its woekly online sales, S(t), in dollars, t weeks after online sales…

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Q: Find the point on the graph of f(x)=√x that is closest to the point (9, 0). (x, y) =

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Q: F 0 f(x) 4. Let g(x) = f(t)dt, wher (a) Evaluate g(0) and g(e (b) Estimate g(x) for x = (c) On what…

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Q: Given that g(x) = f(t) dt use part 2 of the Fundamental Theorem of Calculus to find g(x) for the…

A: ∫tndt=tn+1n+1+cg(x)=∫1x(3t2+6t)dt

Q: Find the particular solution of the differential equation that satisfies the initial conditio f"(x)…

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Q: Determine an equation for a plane through the point: (-7, -9, 4) parallel to the plane 3x + y + z =…

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Q: What amount must be set aside now to generate payments of $30,000 at the beginning of each year for…

A: We are required to find Amount that must be set aside now to generate payments of $30,000 at the…

Q: hy is the derivative of -1/x^2 = 2x-3 and not -2x-3?

A: use the sign given in the function and differentiate it.

Q: Sketch the graph of r = 1 - sin 0 on the graph below. You must plot at least 8 points with exact…

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Q: If f(x) = x² + x and g(x)=x-9, find f(g(x)) and g(f(x)). f(g(x)) g(f(x))

A: Given query is to find indicated composite function.

Q: Use the Quotient Rule to find the derivative of the given function. b) Find the derivative by…

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Q: Suppose a boat leaves port, travels 7 kilometers, turns 21°, and then travels another 12 kilometers.…

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Q: A company determines that its weekly online sales, S(t), in dollars, t weeks after online sales…

A: st=600et If f(x) is a continuous function on interval [m,n] , then it’s average value on [a, b] is…

Q: 3y2-12x-6y-9=0 1. Write in standard parabola form 2. Find the center, vertices, foci, and…

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Q: Use f(x) = 5x − 4 and g(x) = 2 − x2 to evaluate the expression. (a)     (f ∘ g)(x) (b)     (g ∘…

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Q: Consider the following. f(x) x³ + 9, g(x) = √√√x X (a) Find the function (fog)(x). x + 9 (fog)(x) =…

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Q: Suppose f'(x) = x4+x³-6x². Determine the value of x where f has a relative minimum value. (A) -2 B)…

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Q: -1 Ⓡ 6 6

A: To graph the inverse function

Q: 7π Graph the point with the polar coordinates 3, 4 Give two alternative representations of the point…

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Q: A) At x=-1, y" is negative, concave downward, hence, y (-1) is a relative maximum value. B) At x=3,…

A: To solve the following problem

Q: Determine an equation for the plane through the following points: (-5, -9, 3), (-8, -4, 7) and (-9,…

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Q: Evaluate the function at the indicated values. (If an answer is undefined, enter UNDEFINED.) f(x) =…

A: We have to slove above questions

Q: If f(x) = 2x³ + 8 x² + 3, at what points are f'(x) zero or does not exist ? A B (C) 1,0 0, 0, D 0, w…

A: Given query is to find the points where derivative is zero

Q: For which values of a is the matrix singular? [[a,3],[4,12]]

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Q: Given that x = 5 when y = 0, solve the following IVP:  eydy/dx = (2x − 4)

A: Given that       ey dy/dx = (2x-4)

Q: What is the minimal degree Taylor polynomial about x = 0 that you need to calculate sin(1) to 3…

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Q: Compute each of the following values: 4 6² (a) g(x) dx =

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Q: Find sin 2x, cos 2x, and tan 2x if tanx =-3/2 and x terminates in quadrant IV

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Q: 5. Use double integrals to find the volume under the cone z = √√x² + y2 and above the region bounded…

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Q: 1 Find the derivative of the following function. y=5.11* y'=0 Question 1 of 5 >

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Q: The function f(x) is approximated near x = 0 by the second degree Taylor polynomial P₂(x) = 3 + 3x +…

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