šiven r,(t)=sin5ti +cos 5tj+\t+2k and r,(t)=5ti+2k , calculate "[r, (0) •r, (0)]. dt

Q: 1 |dx I (sec² x csc* x.

A: Integration gives the function whose derivative is given. It is nothing but adding all to make…

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

A: Given

Q: Find f. f ''(t) = 3et + 6 sin t, f(0) = 0, f(?) = 0 f(t)=

A: Solution

Q: t' sin(2t n(21*)dt Evaluate

A:

Q: Find div F and curl F if F(x, y, z) = 2eyi- 7 cos y j + 4 sin² z k. div F= curl F=

A:

Q: ) Find y' sin)= 8x+y

A:

Q: Find f. f"(θ)  = Sin θ  +Cos θ , f(0)  =3 , f'(0)  =4

A: Given functionf"(θ)  = Sin θ  +Cos θ , f(0)  =3 , f'(0)  =4we have to find , f(θ)

Q: Find f. f ''(t) = 4et + 6 sin t,    f(0) = 0,    f(?) = 0

A: To find f. f''(t)=4et+6sint,f(0)=0,f'(0)=0

Q: Find y' : In(cos² 3x) = e*+y + sin-1 y

A:

Q: Find the directional derivative of J(, 9) + 3y at the point (2, the direction 57 radians.

A:

Q: Determine order and degree * d'y d'y + cos dr? dr? 2 O 5 undefine- Not linear

A: The degree of a differential equation is the power of its highest derivatives.

Q: Integrate f(cos x)e*+sin xdx B. e-sinx +C A. -et+sinx + C c. ettsinx + C D. e+sinx C

A: Note:∘ddx(sinx) = cosx ∘ddx(a) = 0                                         where a is constant∘∫etdt…

Q: f(x) = cos x + 3, [0, 27], midpoint

A:

Q: Find dx (e3t + 1)dt. -cos(3rx)

A:

Q: Differentiate f(r) = 6x-2 cos z. Answer: f'(z) =

A:

Q: lirectional

A:

Q: Find f. f ''(t) = 4et + 2 sin(t), f(0) = 0, f(?) = 0

A: Find f. f ''(t) = 4et + 2 sin(t),    f(0) = 0,    f(?) = 0

Q: Let f (t) = et sin 8t Part (b) Find C{f (t)}

A: