Let (w, x, y, z) = wxy + x² tan z and a = (1, -2,3,4). Then w(a): .₂(a) = -6 -2 8 60 -8 1-1 2 , (a) = dy(a):

Q: Determine 1 dx , 4x2 +1 (i) (ii) x cos x dx .

A: Determine.  (i).  ∫14x2+1dx             ⇒∫14x2+1dx=14∫1x2+14dx  ⇒∫14x2+1dx=14∫1x2+122dx…

Q: 10. Given: f(x) 3= d) tan(A – B) and g(x)=x² +8 x- 5 Find: a) (f-g)(x) (g •(8))(x) i) (g-f)(3) b)…

A: Given that f(x)=1x-5 and g(x)=x2+8   (a) f-gx f-gx=fx-gx               =1x-5-x2+8…

Q: 6. If f(r, y) = tan-(x/y), then the value of f,(3, 2) is %3D -3 (b) (c) 1 (d) -2 (a) 13

A:

Q: Evaluate Se²x 2x Se²x 2x cos (5x) dx. cos (5x) dx = e2x. (5 sin (5x) + 2 cos (5x)) 19 + C

A:

Q: f(i) = 5, f'(i) = -3i, g(i) = 3i, and g'(i) = 4. Find (fg)'(i).

A: Given fi=5,f'i=-3i,gi=3i,g'i=4. Find fg'i.

Q: Evaluate fa tan() da 1 글 [(22 + 2a) tan-1 ()-피+C o b을[(22+ 2a) tan-1 () + z] +C 2a) tan-1 ()- 피 +C…

A: Solve the above integration.

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 f (x, y) = x(x² + y²)-3/2 esin(a²y) find fa(1,0).

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: If D ⊥ D', D: (2a - 3)x + ay - 2 = 2y + 3a and D': (3a - 1)y + 2(3a + 1)x = a - 1 find the value of…

A:

Q: Let h(t) = tan(3t + 8). Then h'(5) is and h"(5) is

A: As we know that the chain rule: fgx'=f'gx·g'x The Power law: ddxxn=nxn-1   Given: ht=tan3t+8 Now…

Q: Let h(y) = 20 cos y – 3 sin y. Then h'(y) =

A:

Q: L=2-36X, y'co) =5, and ylo)=S x)

A:

Q: y=2(21,2-1 + arctan x) 2 2 x-1

A: Please see the whiteboard.

Q: Let h(x) = tan (2x + 6). Then h'(2) is and h'(2) is

A: topic- functions and derivatives

Q: Find , where : = sin (a²) cos (y*) O 2.r sin (a²) cos (y²) O 2r sin (x²) 6.x sin (a²) cos (y²) 2x…

A: We have to find partial derivative of z  with respect to x.Given a function of two variables, ƒ ( x,…

Q: Find the position vector for a particle with acceleration, initial velocity, and initial position…

A:

Q: Evaluate 2 (y + y cos x)dxdy -3

A:

Q: dy 1- Which one is correct ? The Y of ex?tanx a) (x2 sec?x tanx + 2x tanx) b) (x² sec?x + 2x…

A: Since you have posted multiple questions in this question which are not interlinked so I have solved…

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

A:

Q: 3) S cos(Inx) dx

A: according to guidelines we should able to do only one question at a time #3

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: d (c) (cos(2²) + In(3 – 2æ)) dx

A:

Q: A graph of f (z) =a cos(br) is shown, where b is a positive constant. |(0, 4) (T, 4) |(27, 4) -2…

A:

Q: dy 2 3 ...2 C05X +sinx...y.-(4x+5). y. ---

A:

Q: Suppose r' (t) = (cos(t), et, 2t) and r(0) = (1, 0, 3). Find r(t).

A:

Q: fx = 4y sin(x) and fy = 4y + 4 cos(x).

A:

Q: Q NO3)IF y=Jsinx + Vsinx + Vsinx + . then show that(2y-1) = cosx .And Also Find dx (5vcosx) dx

A: Our objective is to find the derivative of above functions.

Q: 3. _1ffx,y) = tan—1 (), then X c) (x2 +y2)2 is ܐܐܐ )b ܐ)?x +y(

A: The given function is fx,y=tan-1yx. Find the value of ∂f∂y. Here we use the following formulas -…

Q: 5. Find L{f(t)} a. f(t) = sin?(t) + t b. f(t) = n² – 8e¬2t + (et + 1)² | c. f(t) = F, sin yt -cos…

A: As per our limit we can solve only first three subdivisions if you want the answer for other…

Q: valuate f¹² Vsin x + 1 cos x dx.

A: Topic:- application of integration

Q: a) y = 1 √x - √x²+4+tan().

A: To find the derivative of given function

Q: 3+6 b. (2xy-sin x) dx + (x-Cos yldy

A: Topic:- solution of differential equations

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

Q: 6. Find : (a) y = (x³ +5) tan 7x, %3D

A:

Q: Q3) for f(v) = sec2 (3v-1) and g(v) = tan2(3v- 1) show that %3D S(v) = g'(v).

A: