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: 1 Laplace transforms Calculate the Laplace transforms of (i) H₂(t) cosh (3t), where cosh (at) = 1/²…

A: Solution: (i) let, f(t) = H2(t)cosh(3t)                   = H2(t)[(1/2)(e3t + e-3t)]…

Q: Solve the following ODE by determining an appropriate integrating factor to convert the ED to an…

A:

Q: In [tan (5 + )| +o sec x dx 4 2

A:

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: cos (E) U4+ tan(t)

A:

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: 2. 1 Evaluate the definite integrals below. Use u-substitution when appropriate. 4 5 3el/x (a) (b) |…

A:

Q: C. h(x) = 2x² sin(x) - x sin(x) – 15 sin(x); ONLY product rule, NO power rule.

A: Given; h(x) = 2x2sin(x) - xsin(x) - 15 sin(x)

Q: 3. (a) For P(t) = (4t² + 3) (2t³ — t)¹², find P'(t). After taking the derivative(s), do not simplify…

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Q: sin(x) 3h dr. Use the mid-point method | f(x)dr=[f (x0) + f(x1)] to evaluate (b) I-1

A:

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

A:

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: ilf find f'(x). Answer f(x) = 3 sin x 1 + cos a

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Q: Find L {f(t)} if f(t) = cos 5t + sin 2t

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Q: Use the formula £{t^f(t)} (s) = (-1)^(((s)) to help determine the following the expressions. (a) L(t…

A: Solution:-

Q: Evaluate S cot? (r) sec (x) dæ

A:

Q: Jsin(x)cos(x² + 7)dx 2 2

A: Solving the problem

Q: ( (cos(2r) – sin(2x)cos(2x)) -dx =. For +C. What is F (x)? cos(x) – sin(x)

A:

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

A:

Q: solve for y, In - y| +C = (1n|cos(x) – 1| +c)

A:

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: 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: y+y=sin(x), where y(x) = 1.

A:

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: 2x sin-1(x²)dx =

A: This question is taken from the indefinite integral in which we have to choose the correct option…

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: Find the value of f(0) when 3 sin(2t), f( f'(t) 1. f(0) 2. f (0) 3. f (0) 4. f(0) 5. f(0) = = = = =…

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Q: f(t) = -3+4 cos(,(t – 3 ).

A:

Q: If, for V = V (t), tsin(V) = cos(V)+ In(t), then: a) V'(t) = 1 – tsin(V) t(t cos(V) + sin(V)) b)…

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Q: et +e» et Рe-* cosh(x) sinh(x) 2

A: Given that:- coshx=ex+e-x2 sinh(x)=ex-e-x2

Q: Evaluate r(2) and r(-1) for r(t) =(sin~ t, t 2, (t2 + 1)- 1 ).

A: Given:rt=sint , t2, t2+1-1

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.