Find the curvature and the radius of curvature at the stated point. r(t) = 8 cos(t)i+3 sin(t)j+ 5tk; t = NOTE: Enter the exact, simplified answers. K = ||

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A: As we know from the Green's theorem; ∫CMdx+Ndy=∫∫D∂N∂x-∂M∂ydA   Given; I=∫C3x2-ydx+3xdy So, M=3x2-y…

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A: Since you have asked multiple question, we will solve the first question for you as per our guide…

Q: 1. Use the limit definition of derivative (no shortcuts!) to find the derivative of f(x) = 3x² + 2x.…

A: Recall: To find derivative,  f'(x)=limh→∞f(x+h)-f(x)h We have, f(x)=3x2+2x

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A: Area bounded by the curves :    If f(x) and g(x) are two continuous function on a,b and f(x)≥g(x) on…

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Q: In Exercises 5-7, rewrite the specified linear system in matrix form. 5. dx 6. dx 7. dp = 2x + y =…

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Q: Perform

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Q: 1.) lim 5-x 2.) lim 5-x 3.) lim 5-x

A: Given query is to find indicated limit.

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Q: |(sin5 (x)) dx

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Q: 22. Find the function for a parabolic arch that has a base length of 24 feet and a height of 36…

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Q: QUESTION 12 Find d²y/dx². x=1+1²y=t-³

A: Given;  x=1+t2, y=t-t3

Q: Find the derivative of the function. f(x) = (5x + 7)³ (06² +00) ² f1(x)

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Q: Please help

A: Solution: h(t)=12t +18t3/2 -6t2 when it reaches maximum upward velocity h'(t)=0

Q: For the function y = f(x) = x² – 3x − 4, x ≥ 1.5, find df dy y=2

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Q: Find the arc length L of the graph of r(t). r(1) = t³ i+ t j+V6r? k, 2 <t< 5 k, 2 <t < 5 L = i

A: Given : r(t) = t3 i + t j + √6 t2/2 k 2 ≤ t ≤ 5 Now, r'(t) = 3t2 i + j + √6 t k Arc Length :

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Q: Evaluate f (x+3)(x-1) dx

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Q: Evaluate the integral of the following using Miscellaneous Substitution dx 4. Sa

A: We can evaluate the given integral by using the substitution u = x⅙  and the following formulas.

Q: 2. Given the function f(x) = 2x² + 3x + 1, a. Use the secant method to find the instantaneous rate…

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A: According to given,    Let x be length of the portion that is bent into a circle   Therefore, 4-x=…

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Q: Find the area of the region enclosed by the graphs of x = y³ - 14y and y + 3x = 0.

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Q: Find the following using the table below. x 1 2 3 4 4 2 f(x) 1 3 f'(x) 2 3 4 1 g(x) 13 4 2 g'(x) 2 4…

A: Chain Rule of differentiation : fgx' = f'gx .g'(x)

Q: Consider the curve parametrized by a = e-sin(0) and y = ecos(8) for 0 ≤ 0 < 2π. At what points (x,…

A: The parametrized curve x=e-sinθ and y=ecosθ for 0≤θ&lt;2π.

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Q: An isotope of the element erbium has a half-life of approximately 9 hours. Initially there are 7…

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Q: 8. Find the derivative of the function f(x) = x ² - 10x + 3 using First Principles.

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Q: 2. Evaluate the indefinite integrals. (a) fx² - 2e*dx (b) Evaluate (3-4x)¹5 dx

A: We have to evaluate the indefinite integral

Q: * Using the formula sin(bx)] dx = (721 ) eax [a sin(bx) – b cos(bx)] + C a² + b². |[e-8x sin(6x)] dx…

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Q: Let f(x) = Va (2 – x)2. Use the local linear approximation of f (x) at ro V0.99 (1.01)?. 1 to…

A: To use the linear approximation for the given function