||r(t) × r" (t)|| ||r(t)|* Use the formula k(t) to find k(t). 3 r(t) = 7 cos(4t)i+ 7 sin(4t)j+ 5tk K(t) = ||

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: 3i +2V2 - 5n -4i +6(1 +a T/4 [(3sec2 t)i - (5 + sin t)j - (6sec t tan t)k)]dt Find 0. 2 2-57T-4 3i +…

A: ∫sex2xdx =tanx+c∫(constant)dx=x+c∫sint dt =-cost +c∫sect tant dt =sect+c tanπ4=1cosπ4=12secπ4=2

Q: Let f(x) = sin(2x) + cos(x) then f"(x) Select one: O a. 4sin(2z) + cos(z) O b. -sin(2x) – cos(x) Oc…

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

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Q: What is the range of f(x) = cos¯¹(0)? A [-] 2 2 B [0, π] C [-1,1] D (-∞, ∞)

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Q: 1] Evaluate (a) -S (s²+1) ² {t sin (b) S 1/2 5² (s² +¹)² (d) S

A: Find Laplace of tsin(t/2)

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

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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

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

A: Solution:-

Q: Let f (t) = te* +e sin 10t. Find L{f (t)}.

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Q: Jsin(x)cos(x² + 7)dx 2 2

A: Solving the problem

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: cos(x) dx = dx. Use - 0o (1+x²)² o cos(x) 00 cos (x) Compute Jo 1+x²)² dx. Note that 2 (1+x2)2 the…

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

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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: If y = sin x – ln (2x), then dx3 ||

A: The given function is: y=sin(x)-ln(2x)

Q: 1 -x2 + 6x dx = 10 - A In |-x2 + 6x - 10| + C -tan-1(x – 3) + C C -tan-1 (x + 3)+ C D tan-1(x – 3) +…

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Q: f(t) = -3+4 cos(,(t – 3 ).

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Q: // (cos (a? + y³)dA where D: {(x, y) | 4 < x² + y² < 49} Find

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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: ||r′(t) × r"(t)|| ||r'(t)||³ r(t) = 4 cos(t)i + 4 sin(t)j + tk Use the formula ñ(t) = to find (t).

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