Use the formula k(t) = \\r'(t) × r”(t)|| to find (t ||r' (t)||³ k(t) = = r(t) = t²i+t5j 30 t (4 + 25 +6) ²

Q: Given f(x) f''(x) = = = √²* (t³3 + 4t² + 6) dt, 0 (t³ + 4t² + 6) dt, answer the follow

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Q: Calculate r' (t) and T(t), where r(t) = (6 +5t,9 – 61, 2t). r' (t) = ( ). T(t) = ( ).

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Q: The population in millions of arctic founder in the Atlantic ocean is modeled by the function P (t)…

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Q: find (a) r'(1), (b) r"(1), and (c) r'(f) • r"(f).

A: The derivative of a position vector gives the rate of change of position of the body or the velocity…

Q: d dri(t) • r2(t)] = d [ri(t) × r2(t)] dt ||

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Q: AB1: Find g(2), g'(2), and g"(2).

A: Given that gx=∫-2x2ftdt Now we have to find g2, g'2 and g''2 In the interval -2,2, fx=4-x2In the…

Q: Find r'(t), r"(t), r'(t) · r"(t), and r'(t) × r"(t). P(C) = 21²1 - 48 + ²P²H 2³k r(t) 3 (a) r(t) 3it…

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Q: If ƒ(x) = 3x√x + ƒ'(9) = x²√x then ←

A: f(x)=3xx+2x2xwe know  ax×ay=ax+yd dx(xn)nxn-1

Q: f(t)= 140/3 t^2 + 3000 does concavity for f(t) change . t is in days

A: Given : f(t) = 140/3 t2 + 3000

Q: f(t) = (t + 4t + 8)(7t¯² + 6t).

A: Given function is: ft=t2+4t+87t-2+6t-3 Then we get,…

Q: Let F(x) =Cx41D, fCx)=X,and gox)=x+1 True or fals e (gof)(x) = FCX).

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Q: Find r'(t), r"(t), r(t)•r"(t), and r'(t) × r'"(t). r(t)-흑러 - 26 + (a) r'(t) (b) r"(t) (c) r'(t) ·…

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Q: r' (t) × r´ (t) to ||r' (1) × r´ (1)|| Use the formula B (1) = T (1) × N (t) to find B (t) , and…

A: Given that rt=sint-tcosti+cost+tsintj+48k. To find Binormal vector B(t).

Q: What is t' (x) when t(x) = In( ): %3| 2x2+3x+2 Select the correct answer below: O t (x) = 2 + 4x+3…

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Q: Let r(t) = (- Find 7' (t) r' (t) = ( (..) -5 - 2t -3t+3' 5t² - 4 - 3t² -6³-5

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Q: Assume that a store finds that its sales revenue changes at a rate given by S'(1) = -27t? +37t…

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Q: ||r'(t) × r"(t)|| ||r(t)||* Use the formula k(t) to find k(t). 13 r(t) = t²i + t'"j K(t) =

A: Find k(t).

Q: Find r'(t), r"(t), r'(t) · r"(t), and r'(t) × r"(t). r(t) = 2t²1 - 4tj + ²t³k (a) r(t) (b) r"(t) (c)…

A: Note that, according to Bartleby guidelines, we can answer only the first 3 sub-parts in the case of…

Q: f (x) = 3r³ – 9x² 1 + x +3 j(x) = x + 7x + 9 Determine p'(x) given p(x) = f(x)j(x). Please don't…

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Q: Let F(x) = x √ √2+1 dt. Find F"(1) 3

A: Given: F(x)=∫3x t2+1dt Leibniz integral rule for differentiation states that ddx∫a(x)b(x)…

Q: A company determines that monthly sales S(t), in thousands of dollars, after t months of marketing a…

A: Find S'(t)?

Q: Find f. f(t) = f'(t) sec(t) (sec(t) + tan(t)), -2-√2 x Need Help? Read It Watch It - 1/2 < t < 1/₁ (…

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Q: Suppose that f(x + h) – f(x) = 7hx? – 8hx + 5h²x – 3h? – 7h³. Find f'(x).

A: The quotient difference formula is given as, f'x=limh→0fx+h-fxh it is given that…

Q: Solve F (t) = 1 + 2 | F (t- u) e " du. -2u

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Q: a) Let f(x) = √5 + 132³. Find f'(x). f'(2) - O b) Let f(z) J'(x) = 0 evS+13³ Find f'(z). -e'

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Q: Find f'(t) if f(t)= 9t +3t +2. f'(t) = =D

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Q: f(ta (tanx+log secx) e* dx on ((2n-1) T. (2n + 2)2), nez

A: Given that a integration and we solve this integration by general property of integration.   We know…

Q: For f(x) = x? – 2x – 1, find f(2), f'(2), and f(3) – f(2). - a. f(2) = -1 b. f'(2) = c. f(3) – f(2)

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Q: Find r'(t), r"(t), r'(t) · r"(t), and r'(t) x r"(t). r(t) = 5t²i - 5tj + 3t³k 2 (a) r(t) (b) r"(t)…

A: Note: As per the guidelines, I have solved three sub-parts. If you want the solution to the last…

Q: Find (f-1)' (a)   f(x)  = √( x3 + x2 + x +1 ) , a= 2

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Q: ||r(t) × r"(t)|| 13 Use the formula k(t) to find k(t r(t) = ei + e¯tj K(t) = %3|

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Q: Find '(t), given r(t) r' (t) = = -6 5t -5t+3' 5t² +5' -2t² -6t3 3

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Q: Let f(x)= $ (x- 3)* k- 4k+1 8. Find: %| k=0 a) f'(x)= b) [ƒ(x)dx=

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Q: Is the equation t²y' (1) t + 4 - separable? y?

A: t2y't=t+4y2