lim x →0 Jn (x). x" 1 2″ T(n + 1) ¹ where n>- 1.

Q: Integrate 1/(1+x(1/2)) dx

A: Consider the given integral ∫11+xdx. Integrate the given integral with respect to x as follows.…

Q: 3. | (1- 2x) dx 0.

A: Given that, ∫01xdx=12 ∫01x2dx=13 ∫01x3dx=14 The integral to be evaluated is given as, I=∫011-2x3dx…

Q: x*(1 + 2x') dx

A: This is the problem of definite integral with substitution. ∫01x21+2x35dx Substitute 1+2x3=t6x2dx=dt…

Q: d cosh(3x? + 1) and (b) dx d (sinh x tanh x). dx Calculate (a)

A: Given: a ddxcosh3x2+1b ddxsinhx tanhx

Q: How can y = e-x for x >= 0 (and only for x >= 0) be sketched?

A:

Q: A ( sinh x- coshx tanh e 6)

A: You all need to have the idea of hyperbolic and their basic calculus.

Q: 7. Let y = tan (3x - 2), find y'.

A:

Q: Find dy/dx. x = t/(9+t), y = (9+t)^(1/2) dy/dx = ?

A: We have to use the parametric form of differentiation . In parametric form of differentiation , we…

Q: 4. lim x? = 4 x-2 Ans: Delta = Epsilon/5

A:

Q: 10. Show that y = 2x³ – 5x satisfies y' + y" - xy" + 5 = 6x² [T:3]

A: We have to show that given condition in question.

Q: P(ze <z < 0)=0.390

A: From the provided information, P (ze &lt; z &lt; 0) = 0.390

Q: Evaluate -o (i +1) 3° ui = 0

A:

Q: Calculate dy/dx. You need not expand your answer. y =x2.3/9+2/x2.3)(9x − 1) Answer ----->dy/dx:…

A:

Q: The value of (i)' is = ... O T/2 O T/2 O e^(-T/2) O e^(Tt/2)

A:

Q: العنوان > solve b cos (ln x ) d x (1-X²) X' 5/2 dx ۱/۱ S で T=T M

A: Here the integration formula has been use∫uvdx=u∫vdx−∫(dxd​u∫vdx)dx

Q: +/t%edt 1. 2. Se-x/2dx 3. 3*e*dx

A:

Q: Lisedydx

A: We need to evaluate ∫-10∫-x1y2 exy dy dx The region of integration is given as Here -x≤y≤1-1≤x≤0

Q: y = In(sec x + tan x)

A: Solve the above differentiation.

Q: tanh-(x) + sech-1 1+x2 %3D

A: Given function

Q: If h (z)=3-2x+5 ln (z+4) then determine h' (1). h' (1) = Number

A: h(x)=3-2x+5lnx+4d dx(xn)=nxn-1d dx(constnat)=0d dx(lnx)=1x

Q: x² + 3 x6 – x² + 7x + 4 10. +x*e*(sinh x – cosh x + e*)| dx

A: We want to evaluate ∫x2+3x6-x2+7x+4+x2exsinhx-coshx+exdx. Since…

Q: 3. Find the derivative D(x *arctan(x)) And the integral 6x dx 9+x

A:

Q: (e* + 1)ydy = (y + 1)e*dx

A: Given differential equation is (ex+1)ydy=(y+1)exdx⇒ydyy+1=exex+1dx⇒1-1y+1dy=exex+1dx