Finding Surface Areas 1- Find the lateral surface area of the cone generated by revolving the line segment y = x/2,0 ≤ x ≤ 4 about the y-axis. Check your answer with the geometry formula Lateral surface area = 1/1/12 X base circumference X slant height. 2- Find the surface area of the cone frustum generated by revolving the line segment y = (x/2) + (1/2), 1 ≤ x ≤ 3, about the x- axis.

Q: 4 √25-x² X 3 dx

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Q: Determine if 1781 is divisible by 3, 6, 7, 8, and 9.

A: Determine if 1781 is divisible by 3, 6, 7, 8, and 9

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A: Let u=tan-1(2t)⇒dudt=21+(2t)2=21+4t2⇒du2=dt1+4t2 ∫etan-12t1+4t2dt=∫eudu2…

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A: Given problem:- f(x) = (x-2)/(x+2)2 Find the maximum and minimum limits of the function

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A: Given that differential equation is exact hence we have to find the solution of this equation .

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A: Given that            function f(x) = 5x4-2x2+8x-3     Now             f'(x)    =  ddx5x4-2x2+8x-3…

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A: Let's evaluate given R2-R functions limit.

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Q: Solve: 123 1 224 + 1 315 - 4x6 +...? +

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A: Topic = Derivative

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A: Please see the below picture for detailed solution.

Q: ) Write a MATLAB code for solving the following equation : N Y = [i+x i=1

A: MATLAB code

Q: Q3/ Evaluate four of the following integrals. ( x³+1 sinx cosx dx b. f*+¹ dx c a. S √1+cos2x x²

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A: We have to find value of given definite integral.

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A: We have to find the average rate of change.

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A: topic - coordinate conversion x=rcosθy=rsinθ

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Q: consider the function y=−3sin(4x−π/2)+1  A) Graph the function over exactly two cycles. (Describe)…

A: We have to graph the given function.

Q: The proper way to evaluate f (3 + h) for the function f(x) = −4x² + 3x − 1 is Of(3+h)=(−4(3)² + 3(3)…

A: We can answer the question as below.

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Q: Find all critical points of f(x) = 3 + 12x - x² and use the First Derivative Test to determine…

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Q: Directions: Using Fundamental Theorem of Calculus (FTOC), compute the following definite integrals.

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Q: Scoth (2) dx

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Q: In t years, the population of a certain city grows from 500,000 to a size P given by P(t) = 500,000…

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Q: Use power series operations to find the Taylor series at x = 0 for the following function. 7x² −14+…

A: Taylor Series expansion of 7x2-14+14cosx at x=0

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Q: Consider a right triangle with a side of length x opposite angle A, a side of length y opposite…

A: Consider a right triangle with a side of length x opposite angle A, a side of length y opposite…

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A: Topic = Derivative

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A: Given

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