r' (t) × r´ (t) to ||r' (1) × r´ (1)|| Use the formula B (1) = T (1) × N (t) to find B (t) , and then check your answer by using the formula B (f) = find B (t) directly from r (t) . r (1) = ( sin 1- t cos t) i+( cos t+ t sin t) j+48 k Enter the vecto s í , the vector j as f, and the vector k as k. ria B (t) = | ? ? Edit

Q: ||r'(t) × r"(t)|| ||r(t)||* Use the formula k(t) to find k(t). 3 r(t) = 4 cos(7t)i+ 4 sin(7t)j + 3tk…

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Q: Find F(t) such that F'(t) = sec³ (t) tan³ (t) and F (3) = 0.

A:

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

A: Given: The vector r(t)= a cost i + a sint j+ ct k   (a≠0, c≠0)

Q: cos 2x dx (b) 4 cos t dt 0 2

A: Since you have posted multiple questions, we will solve only first question for you. To getremaining…

Q: If 7'(t) = (cos t, e2t, 3t²) and r(0) = (3, 1, –2), find the function 7 (t).

A: Given. f'(t) = (cos t , e2t , 3t² ) To calculate the vector function are we need to integrate the…

Q: L{t sin t cos t} = 2s (A) (s²+4)2 -2s (B) (s²+4)² (C) 14) (s²+4)² -8 (s²+4)2 (E) (s²+4)²

A:

Q: f(x) = 3x cos ƒ'(x). -1 (2x + 4) − √√/19 − 3x², find

A: Given: fx=3xcos-12x+4-19-3x2. To Find: f'x.

Q: Find L{f(t)} by first using a trigonometric identity. (Write your answer as a function of s.) f(t) =…

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Q: ; Choose the most appropriate answer. (i) Let 1-r 2 E (an cos(ntx) + bn sin(nrx)], n=1 on (-1,1).…

A: This is Fourier series expansion of (1-x) from -1 to 1.

Q: Find f. f "(t) = 8e + 8 sin t, f(0) = 0, f(n) = 0 8e' + 8 sin (t) + 8 – 5e" -t - 8 f(t) = | Need…

A: Solve intial value problem ( IVP)

Q: V sin2(x32 - 1) dx, with u x32 - 1

A: Consider the integral ∫(√x)sin2 (x3/2 - 1) dx.

Q: Find r'(t). cos 4 cos³(t)i + 2 sin³ (t)j + k r(t) = 4

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Q: Evaluate S cot? (r) sec (x) dæ

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Q: Jsin(x)cos(x² + 7)dx 2 2

A: Solving the problem

Q: Find F(s). F(s) = L(1 et + 3e-4t) cos(2t)} -

A:

Q: Use the cosine law to show that ū · ở = ||ū||||J|| cos(0). You must use the cosine law in this…

A: To prove that               u→·v→=u→v→cosθ

Q: Find f. f(t) =|| f"(t) - 3et+ 5 sin t, f(0) = 0, f(T) = 0

A: To find f.f''t=3et+5 sin t, f0=0, fπ=0

Q: Determine if each statement is true or false. If a statement is false briefly explain why it is not…

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Q: MacB = (x),ƒ o (1)fp хр = (x),f o %3D (x)fp = (x),f O %3D xp = (x),f o = sin x, which of the…

A: To find the correct option.

Q: -2t L{e cos? 21

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Q: f(t) = -3+4 cos(,(t – 3 ).

A:

Q: f (t) =-e" sin (21 +7)

A:

Limits

When it comes to calculus, limits are considered to be a very important topic of discussion. The main importance of limit lies in expressing the value of a function as it gets closer to a certain value. Also, limits can help you to understand other topics, such as continuity and differentiability better. In a broader sense, every calculus notion is a limit. Other branches of calculus have also been derived from limits.