If x= Arctant, y=. 2ay" =17 when t=V2. 1+76, find the value of a if y' В © VE E -2/2

Q: S In(sin(x))dx

A: Given, I=∫lnsinx dx To evaluate I.

Q: If VT + Vy = 10 and the point (4, 64) is on the curve, find dy x=4 by implicit differentiation. dx…

A: Given that: x+y=10

Q: For which values of x are y = sinh x and y = cosh x increasing anddecreasing?

A: Hence, sinh x is increasing for all x.

Q: Suppose that a company can produce 12000 units when the number of hours of skilled labor y and…

A:

Q: if f(x)=2x-cos(x), Use Newton's method to approximate x, starting from the initial value xo=0

A: Solution:-    fX=2x-cosX           x0=0    f'x=2+sinxwe know      x1=x0-fx0f'x0           =0-f0f'0…

Q: Find the approximate value of √0.95 using differential

A:

Q: A particle moves along the curve y = x^(3/2) in the first quadrant in such a way that its distance…

A: Let (x,y) is a point on y = x^(3/2)Distance of (x,y) from (0,0) is given by:

Q: Find th epwation of the tangent line to An- (x-2y): 2xy-1 at print (1, 2) d [sin- (x-2g)] = (2xy-1)…

A:

Q: Find the first derivative: y = In sin e Oy = 2e sece Oy = -2e cot e= Oy = 2e tane Oy = 2e cscez

A: Solve by derivation

Q: S" S"(sinx + cosy) dx dy

A: our objective is to evaluate the integration

Q: If x = tan - log y a d'y dy Show that (1+x²)- +(2x- a)-0 dx dx?

A:

Q: Find the equation of tangent at x = In 5: ln 2x a) y = ²x + 1 e to :

A: According to our guidelines, In case of multiple questions we are supposed to answer the first…

Q: From the figure formed in integrating -dx, what is the term or value that is adjacent to the angle .…

A:

Q: Find the equation of the line tangent to the graph of y = arctan (sinh(r)) at z = 0. %3!

A: Given: y=arctan(sinh(x)) Since, ddxtan-1fx = 11+fx2f'x Therefore, dydx=11+sinh2xcoshx

Q: If y = ln(tanhx), find dy/dx.

A:

Q: Hiw proo p. s (sinh at) =_a s- at Notes at

A: Explained below

Q: 5 dx, correct +2x²) Problem 19. Evaluate (3 to 4 decimal places

A: ∫0152x2+3dxSubstitute u=2x3→dudx=23→dx=32du=∫532(3u2+3)duSimplify:=523∫1u2+1duWe know that…

Q: Solve for the following implicit derivative: d²y si sen(y) = ycos(2x) dx?

A: We have to find the double derivative of the given function.

Q: dy y(ln y – In x +1) dx 1 C = -In None of the choices Option 1 1 C = -In C = -In- -ln Ontion3 Ontion…

A:

Q: Find the differential equaiton corresponding th y= a cos(log x) +b sin(log x) where a and b are…

A: Differential equation formation

Q: TT sin 5. Approximate dx by Simpson's rule with seventh ordinates?

A: Simpson's Rule:    ∫abf(x)dx=∆x3f(x0)+4f(x1)+2f(x2)+...+2f(xn-2)+4(fn-1)+f(xn) Where, ∆x=b-an We…

Q: S) - aresin 2. 2 arcsin 2. is constant for 0sxs 4.

A:

Q: B. Use the trapezium rule with 6 ordinates to estimate fe* dx correct to two decimal places.

A:

Q: The acceleration of a particle moving along the x-axis is given by a(t) = (1-8)sint for 0 ≤1≤ 8. At…

A:

Q: dy Find by implicit differentiation. 20x = 20 - ey ... dx (Type an exact answer.)

A:

Q: L{ e¬at sinh wt} =

A:

Q: 4. If a point is moving along y = 3x2- 4x – 6 at a rate of = 4 m/s, find dt when x = 3.

A:

Q: If xy-In(3 sinh(3x)) , then x? y'-

A: Given,           xy=ln3sinh3x

Q: Find dy by Dx when y is equal to under root  2x²-5x+n whole cube

A: Given: y=2x2-5x+n3

Q: find dy / dx for Hhe tellowing in (sec EX) In (cosp?}

A:

Q: Find the differential of the function. y = sqrt(1+ln(z))   dy=?

A:

Q: Find , if y = x sinh x - cosh x %3D dx

A:

Q: Find an equation of the tangent line to the gra 26. 1+ln(xy) e (1, 1)

A: Obtain the derivative of the function with respect to x as follows.

Q: IF x = asec'0 and y = atan '0 dy Find at 0 dx 3

A:

Q: ■ Find dy /dx  by implicit differentiation 4 cos x sin y =1

A: To find dy/dx

Q: From the figure formed in integrating -dx, what is the term or value that is adjacent to the angle…

A: Given:    ∫x2-3xdx

Q: Use the composite trapezoidal and Simpson's rules with step length h = 0.4 to estimate In(2+3/x)…

A:

Q: 10. S V9x2 + 64 11. ( sech?(In x) 12. S cosh(5x – 7) dx

A: Given

Q: show that d/dx arctan (tanhx) = sech (2x)

A: On differentiation, we get

Q: dy Find by implicit differentiation. dx 14 In x= 18 - In y dy dx (Type an exact answer.)

A: Consider the given expression 14ln x=18-ln y.

Q: Use the composite trapezoidal rule with the step length h = 0.1 to evaluate sin x = 5.² in six…

A: Given integral is ∫0πsinxxdx. We have to evaluate the given integral by using composite trapezoidal…

Q: If y= tanu, u=v-- -, and v=ln x, dy at x= e? dx what is the value of

A:

Q: 16 Evaluate ſ," x²In 3x dx correct to three decimal places.

A: Given- ∫12x2ln3x To find- The value of the above integral. Concept Used- The above integral can be…

Q: The length of one arch of the curve y = sin x is given by L = | VI + cos² x dx. 0, Estimate L by…

A:

Q: find the antiderivative of dx/sqrt(ex-1)

A: To find : The antiderivative of dxex-1 Solution The antiderivative can be evaluated as, ∫dxex-1 Put…

Q: Differentiate y=arccos(e^(3x)) dy/dx=____________

A:

Q: 3- Coshx dy +ly sinh x +e) dx

A: We have to find the solution of differential equation

Q: A new fast-food firm predicts that the number of franchises for its products will grow at the rate…

A: Given

Q: dy y(ln y – In a + 1) dx 1 C = -ln C = -In Option 4 O option 2 1 C =-In

A: This question is based on solution of differential equation.