r1(t) = 3ti + 3tj + t°k, r2(t) = t'k d [ri(t) r2(t)] = dt

Q: Find f. f'(t) 8 cos(t) + sec?(t), -7/2 <t < a/2, f(a/3) = 5 f(t) =

A: Given

Q: dt = (c) (9+t2)3/2

A: Given:

Q: Find f'(a). f(t) = t – 9t

A:

Q: F(x, y) = (2x + y3, 3y - x4} across the unit circle

A:

Q: du = t2 + 3u, t> 0, u(5) = dt 100

A: Given differential equation tdudt=t2+3u and u5=100 ⇒tdudt−3u=t2⇒dudt−3tu=t2t⇒dudt−3tu=t Hence, the…

Q: Find f. f'(t) = 2t – 2sint, f(0)=7

A: From the given problem: f't=2t-2sint And f0=7

Q: Find and from: 3. x = V1-t and y = t³ – 3t

A: Since, you have asked multiple question, so as per company guidelines, we will solve the first…

Q: h(t) = 4e5t-7t-3 Determine the value of h'(-1).

A: Given query is to find indicated derivative.

Q: f(t) = 5e-2t + calculate the LT. +² 2'

A: Laplace transformation of the function

Q: (c) Differentiate y = Vsec3 (5t2)

A:

Q: Find r'(t), r"(t), r'(t) · r"(t), and r'(t) x r"(t). - r(t) = 3t²i – 4tj + ²t³k 2 (a) r' (t) (b)…

A:

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) ·…

A:

Q: Calculate r' (t) and T(t), where 1668 T(t) = r(t)= (4t-4, 1- 4t, 6t – 1).

A:

Q: dy If y = (t + 2t + 5) (7Ł² + 3), find dt dy dt

A:

Q: Find y as a function of t if y (0) = 7, y'(0) = 3. y(t) = 25y" +50y + 106y = 0,

A:

Q: F(x) = 9t dt

A: given: Fx=∫0x29t dt Fx=∫0x29t dt=9∫0x2t dt=9t1+11+10x2=9t220x2=92t20x2=92x22-02=92x4-0=92x4

Q: d -e'(t² + 5) at t = 0. dt Find

A:

Q: Find the function r that satifies the following condition. r'(t)=(3t2,4t3,2t); r(1)=(-2,-5,-9)…

A: Given,          r't= 3t2 , 4t3 , 2t  , r1=-2,-5,-9

Q: Find F(t) knowing that F'(t) = (t²,4t³, -t²) and F(0) = (0,1,0).

A:

Q: If y = (t² + 2t + 6) (3t² + 5), dy find dt dy dt ||

A: Given function: y=t2+2t+63t2+5 To find the derivative of y with respect to t that isdydt. Formula…

Q: Calculate r' (t) and T(t), where 88.8 r' (t) = ( T(t) = ( r(t) = (3t6,2 - 3t, 2t - 9).

A:

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

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Q: a fif f" (t) = 2e* +3 sin(t), f(0) =-8, ) =

A:

Q: Find f.  f''(t)=sint+cost,    f(0)=1,    f'(0)=2f′′(t)=sint+cost,    f(0)=1,    f′(0)=2   f(t)=

A: Given as f"x=sin t + cos t integrate both sides then f'x=cos t-sin t+CPut f'0=2Thus2=1+C⇒C=1 Thus…

Q: dy If y = (t² + 7t + 5) (2t² + 6), find dt

A:

Q: Dy/dt = 2y(5-y) is the equation autonomous?

A: An autonomous equation is a differential equation in which the independent variable does not appear…

Q: Find f. f"(t) = 5et + 4 sin t, f(0) = 0, f(1T) = 0 f(t)

A: topic- differential equation

Q: -3x2 F(x) = S*" t² dt %3D

A: TO EVALUATE THE FOLLOWING INTEGRAL F(x) ∫-x3x2 t2 dt FORMULA USED- ∫abxn dx = xn+1n+1 i.e substitue…

Q: dy If y = (t² + 5t + 8) (3t² + 2), find · dt dy dt

A: given  y=(t2+5t+8)(3t2+2)dtndt=ntn-1