1. Let f() J-x-sin a +2x V sin“t +1 dt. (a) Show that f (x) is strictly increasing. (Hint: compute f'(x)) (b) Compute f-1(0). (c) Compute (f-1)'(0).

Q: find the integrating factor of cos(x)y'+sin (x)y=2cos^3(x)sin(x)-1

A:

Q: A more detailed version of Theorem 1 says that, if the function f(x, y) is continuous near the point…

A:

Q: 3. (a) Determine f 2xe3*dx by using integration by parts. (b) Determine S cos(x²) 2x dx by using…

A:

Q: Given f(x) = 8x3 + In(x – 1). Estimate the value of f(2.01) using differential. %3D

A:

Q: That the value of the integration g(1) = 0, g(2) = 0 1-e) -dt where g is a function that is…

A:

Q: Find the differential dy of the given function. y = In√9-x² dy =

A: Given y=ln9-x2 Formula: ddx(ln u)=u'u where u is a function of x Now consider y=ln9-x2 The given…

Q: 3. (a) Compute ,12x – 1| dx in two ways. i. By using properties of the definite integral and the…

A:

Q: z = x siny + y sinx

A:

Q: A more detailed version of Theorem 1 says that, if the function f(x, y) is continuous near the point…

A: Explanation-  Given that, The initial value problem is- dydx=x2-y2 ; y0=1 Here, The function is-…

Q: 1 Evaluate the improper integral dx. (x – 3)3/2' 3 -

A:

Q: A more detailed version of Theorem 1 says that, if the function f(x, y) is continuous near the point…

A:

Q: Determine | An (x) An+1(x) dx, from the relation: tn .1 Σ (2n + 1)! tn+1 A, (x) An+1(x) dx n=0 n -1

A:

Q: Find the linear approximation of f(x) = ln x at a = 1 and use it to estimate In(1.2). L(x) = In(1.2)…

A:

Q: If f(x) = A B (C) tanx S 0 sec ³x 1+e tanx 1+tan²x 1+ e tanx 1+12 sec²x 1+e tanx In (coor) 1+ e'…

A:

Q: A more detailed version of Theorem 1 says that, if the function f(x, y) is continuous near the point…

A:

Q: 3. Write the exact differential: f(x,y)=e-y-el-

A: Given- fx,y=ex-y-ey-x To write the exact differential.

Q: Find the solution of the differential equa­tion that satisfies the given boundary condition(s) .  f"…

A:

Q: 5. x- + Px = sin t %3D dt

A:

Q: Let y 5x²8x + 4. If Ax = 0.1 at x = 1, use = differentials to estimate Ay Ay ~

A:

Q: s+a Using differential and integration of transforms, find f(t) if L[f] equals In s-a

A:

Q: Consider the following differential equation. (sin(y) – y sin(x)) dx + (cos(x) + x cos(y) – y) dy =…

A:

Q: 1.1 the integral f cos(lnx) dx . x2 1.2 the integral S x³V1– 2x dx

A: 1.1 Given integral is ∫coslnxx2dx Let u=lnx⇒dudx=1x dx=xdu1x=e-u∫e-ucosudu we will integrate by…

Q: A more detailed version of Theorem 1 says that, if the function f(x, y) is continuous near the point…

A:

Q: 4 2 1 Evaluate || - dy dx by reversing the order of the integration. O V Y +1

A: Given:∫04∫x21y3+1dydx

Q: From the differential equati on by eliminating the arbitrary function ffrom xyz = f (x?+y'+z°).

A:

Q: A more detailed version of Theorem 1 says that, if the function f(x, y) is continuous near the point…

A:

Q: Find the differential dy of the given function. y = In√√/9-x² dy =

A:

Q: Example 11: 3 If F(x) = J Int dt, find F'(xr) 2+sin 2.x

A: To determine the F'(x).

Q: Use at least two methods to prove that dr/dt=0 when r=√x2 + y2, x=α cos t, and y=α sin t if α is a…

A: First method   r=x2+y2r=(α cost)2+α sint2            since x=α cost and y=α sint  =α2cos2t+α2sin2t…

Q: 7 Integrate by using the Archimedes-Riemann Theorem | (2.02 + x)dx

A:

Q: dx J x2-4x+5

A: Since you have asked multiple questions, we will solve the first question for you. If you want any…

Q: Evaluate the Integral dx – (**V2Tan-1x-(Tan-1x)2 1-х4 '2Tan-1x-(Тап-1x)2 3. S х?/2Tап-1x- (Тап-1x)2…

A:

Q: 11. In line integrals, if x(t) has a derivative equal to 0, with y'(t) and z' (t) not equal to 0, A.…

A: To Select: The correct the option(s): 11. In line integrals, If x(t) has a derivative equal to 0 and…

Q: If the function f(x) is defined on the 2 intervallo, TT) and f'(x) = -cos X (sinx) than f(x) has…

A: Given that fx is a function defined on an interval 0,π whose derivative f'x=-cosx1+sinx2 To find the…

Q: 8. Compute the differential df of f(x,y) = log (x² + y²).

A: Given; f(x,y) = log(x2+ y2)

Q: Suppose 4x + 9y - 25, where x and y are functions of t. (a) If dy/dt-, find dx/dt when x = 2 and y =…

A: Given: 4x2+9y2=25 Since, x and y are functions of t, therefore differentiating each sides with…

Q: Find the number N such that the differential (y^3-2x)dx+Nxy^2dy is exact

A:

Q: 11. In line integrals, if x(t) has a derivative equal to 0, with y'(t) and z'(t) not equal to 0, A.…

A:

Q: A more detailed version of Theorem 1 says that, if the function f(x, y) is continuous near the point…

A:

Q: find / sin³ x cos³ x dx cos³ 2x sinº 2x dx 11. 12. cos² x dx sin? x dx 13. 14. 16. 7 sin y dy 7 cos'…

A:

Q: Evaluate the curve f(x, y) = 0 which passes through the point (0,4) and satisfies the differential…

A:

Q: Compute the differential dz of the function. 6.7 Z = x dz ||

A: Here, to find the differential dz of the function z=x6y7 Note that: dz=zxdx+zydy...(1)

Q: A more detailed version of Theorem 1 says that, if the f f(x, y) is continuous near the point (a,…

A: Given: (15). dydx=x-y (16).dydx=x-y

Q: 2. Prove that g(x) = sinh x + x – 1 has a zero in [0, ln 2].

A: To prove that gx=sinh x+x-1 has a zero in 0, ln 2.

Q: Find fyxyx for f(x, y) = ln(xy) − cos (xy) at (1, π)

A:

Q: integral of C(1-e^(-bt)) with the initial time being 0

A: Let's find.

Q: 4. Express the integral e-t tổ dt in terms of gamma function.

A:

Q: Let x > 0 and b > 0. Show that

A:

Q: Find the antiderivative of f(x) = point (0,3). O F(x) = tan¹x +1 O F(x) = 2 tan ¹x +1 -1 O F(x) =…

A: Given: fx=24x2+1 and x,Fx=0,3   As we know the expression for the antiderivative; Fx=∫fxdx And…