14. Simplify the following functions using the properties of logs. a) f(x) = ln (e5x) - 3x + 5 ln(1) b) f(x) = ln + ln (4) + Inex - elnx

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A: Given: I=∫xcos4πx2dx   ...1   Use the common integral: ∫cosxdx=sinx+C

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Q: Which equation choice could represent the graph shown below? -10 9 8 7 -5-4-3/2 -1 Of(x)= x(x +…

A: We will find the required.

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Q: dors de lim (3x - √90c²-5x+7 84∞

A: Topic - Limits We are given limx→∞3x-9x2-5x+7

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Q: Find the indefinite integral. (Use C for the constant of integration. [x² x cos 7x² dx

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Q: The graph of f is shown. Evaluate each integral by interpreting it in terms of areas. y (a) 256 (c)…

A: Topic = Area

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Q: 9. Use the properties of logarithms t a) f(x) = ln (e-2x) + 3x + In b) f(x) = ln (²) + ln 4 − elnx -

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Q: Use l'Hôpital's rule to find the following limit. lim 9x² e-x X→∞

A: To evaluate the given limit of the function

Q: Find the indefinite integral. (Remember to use absolute values where appropriate. Use C for the…

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Q: Find the following using the table below. X f(x) f'(x) 1 2 3 4 +3+ 4 g(x) 2 g'(x) 4 1 2 -~-~ -33 1 2…

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Q: 1. Suppose f is differentiable everywhere, f(0) = −1/2, and f' is graphed below. 1 X پر 2+ (a) Find…

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Q: Find the indefinite integral. (Remember to use absolute values where appropriate. Use C for the…

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Q: find the accumulated amount after 3 years on an investment of 5000 earnings an interest rate of 5%…

A: given query is to find accumulated amount.

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Q: (b) lim ex xxx

A: Let's evaluate the given limit.

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A: Given is to find the formula for nth term

Q: 4 2 -5 -4 -3 -2 -1 -2 -4 -6 -8 -10+ 1 2 e function graphed above is: cave up on the interval(s) cave…

A: The function is concave up where -2<x<1.   The function is concave down where 1<x<5.

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Q: 7) A triangular plot of land has one side along a straight road measuring 300 feet. A second side…

A: A triangular plot of land has one side along a straight road measuring 300 feet. A second side makes…

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Q: Find the surface area of the part of the plane 5x + 3y + z = 2 that lies inside the cylinder x² + y²…

A: Plane: 5x+3y+z=2 Cylinder: x2+y2=4

Q: Evaluate the definite integral. Use a graphing utility to verify your resul f. ²xe-7x² dx

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A: Given that sinhx=-125Our aim is to find the value of cschx=?

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Q: Determine which graph is the graph of f(x) if the following are true. = 0. f(x) has a horizontal…

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Q: vinnnnn 2. Use sigma notation to write the Taylor series about Xo =1, for Inx.

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Q: π 5) Find the exact value of sec- 8

A: Consider  secπ8   Formula  secx=1cosx

Q: A triangular plot of land has one side along a straight road measuring 300 feet. A second side makes…

A: Let, AB be the road. The side AC makes an angle 53 ° and side BC makes42° angle with the road.

Q: Which of the following integrals is the area between the graph of f(x) and the y-axis from 0 to 6…

A: Note: Since, there is a typing error in "the area between the graph of f(x) and the y-axis" because…

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A: Distance along the shore= 40m Distance from the shore= 50m Run speed = 4 m/sec  Swim speed = 0.9…

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Q: QUESTION 3 2-1 Find parametric equation of line == +2 22=2²=== y + 3z = 23 Hence find its…

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