%3D or False: If y=lne, then y'= 1? Explain

Q: 1. ſ ev¤dx

A: As per rule of bartleby we can solve only one question at a time and we can solve only three subpart…

Q: Find cosh 2x sinh? 2x dx.

A:

Q: Sar en x² dx Given: Find: Formula o fe"du Sa"au

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Q: e sinh 2x dx

A: The given integral,       ∫e-xsinh(2x) dx

Q: 2. A spherical snowball melts at a rate of 367T in /sec. At what rate is the radius of the snowball…

A:

Q: 44. y" +y = secr· csc x

A: Consider the equation, Let the homogeneous equation is The standard form of this equation is The…

Q: (x?1) ore sin2x dx

A: Integrate by parts: ∫f(x)·g(x) dx = f(x)·∫g(x) dx - ∫df(x)dx·[∫g(x) dx] dx +C

Q: Find [sinh-(cotx)] and simplify completely. d dx

A:

Q: 4-S cosh? Vx dx x csch vx

A:

Q: S csc6 3x dx 9° S cot5 x dx dx cos* 6x

A: We know that csc2θ - cot2θ = 1 sec2θ - tan2θ = 1

Q: 32. Vx arctan x/2 dx

A:

Q: S tan — х) dx

A: To integrate: ∫tan(x4-x)dx Solution: Given, ∫tan(x4-x)dx On simplifying further we get:…

Q: 11. Evaluate dx if possible. If not possible, explain why. Vx? – 9

A: The objective is to evaluate the integration.

Q: 5. Sx? cos 6x3 dx %3D

A: We have to evaluate the given integral by using theorems of antidifferentiation.

Q: Find y' if cosh x sinh?

A:

Q: 2. I cosh ix dx

A: The given integral is ∫cos14xdx. Evaluate the integral.

Q: he acute an e first and se

A: Given that, Length of first leg = a = 10 ft Length of second leg = b = 24 ft Therefore the length of…

Q: Scin'se dx

A: In this question we have to find the Integration.

Q: dy 200 ky ln dx y

A: This is the problem of dynamical system.

Q: 13h dn.

A:

Q: 15. x²y' + 2xy = ln x, y(1) = 2

A: Consider x2y'+2xy=lnx, x2dydx+ydx2dx=lnx Use the product rule of differentiation. dx2ydx=lnx

Q: So Si S*x 1 су-х ху dzdydx

A: Let the integral be  I = ∫01∫x1∫0y-xxydzdydx 'I' can be solved directly by integrating individual…

Q: (coshx – sinhx)? dx =

A: To evaluate the given integral.

Q: 3. Stan tan³ 3x sec ¹ 3x dx

A: As per our company guidelines, we are supposed to answer only one question. Kindly post other…

Q: e of x in units?

A:

Q: 5: - S cos(lnx).dx

A:

Q: y = [log(arc cot r3)]cosh

A:

Q: dy 5. х dx - (1 + х)у %— ху?

A: The methods and formulas to find the solution of the Bernoulli equation help to find the required…

Q: | arctan x dx=?

A: We evaluate given integral

Q: 10. S sinh rai tanhxainhr-tenha -dx

A:

Q: 2. * Evsluate O 4 | dx Evoluate @ 12-X

A:

Q: 7. A vertical cylinder is leaking water at a rate of 1 ft'/sec. If the cylinder has a height of 10…

A: To find the rate of change of height of water changing

Q: In the Newton's Law of Cooling, at small differences of temperatures between the body and the…

A: Recall:  The rate of loss of heat is directly proportional to the difference in the temperatures…

Q: coth3x dx sinh3x

A: ∫coth3xsinh3xdx=-cosech3x3+C           where C is an integral constant.

Q: tanx dx

A:

Q: Sodium chlorate crystals are easy to grow in the shape of a cube by allowing a solution of water and…

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Q: Find appropiate in tegrating and solve the equation an 3 323? dx + こ

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Q: Find the numerical value of a) sinh Cen 4) b) sinh (1

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Q: 7 dx = x3

A: ∫xndx=xn+1n+1+C1xn=x-n

Q: Bearing of YZ? SL E ? 135°

A: we have to determine the angle of bearing yz

Q: Differentiate y = e9 tan E

A: y=e9tanxy'=e9tanxddx(9tanx) [chain rule]y'=e9tanx×9ddx(tanx)y'=9e9tanx·sec2xddx(x) [chain…

Q: In (x) -dx is equal to x2 The numerical value of

A: Given is an integration and we have to find it's numerical value. Here, we use the Integration by…

Q: 2VIn 3 •VIn 3 35. dx dy ly/2

A:

Q: +y (cotx) = 5e* dx

A: Given;

Q: S tan* dx

A: Using , Trigonometry formula and integration rule

Q: 1 СА СВ + 1 DA DB 11 1 MA MB

A: if ABCD = -1 then ac/cb = ad/bd MA = MB since m is the mid point of AB DA DB + CA CB / (CA CB DA DB)…

Q: S(sech²(cosh3Ø)sinhø dø

A: According to question given :∫(sech2cosh3ϕsinhϕ dϕ

Q: Write Dn E and Du E using

A: Given that D=v|v>1    and  E=v|v≤8. D∩E=v|v>1  and  v|v≤8=v| v>1  and  v≤8=v|  1<v≤8…

Q: ans arccos(x + 7) = arcsec(x)

A: