1. If y= tanx, prove that y"=2(y² +1)(3y² +1).

Q: Compute cosh x and tanh x, assuming that sinh x = 0.8.

A: Here given as sinhx=0.8 Use the identity…

Q: . If y = tan( sin t (. cos t-1 1 dy %3D show that dt 2

A: The given details are as follows. y=tan-1sin tcos t -1 Observe the chain rule of differentiation as…

Q: a if y = In (sinh 50) and x = 7. cosh 40

A: We have given y and x and we have to find out dy/dx

Q: Use Green s theorem to evaluate the give (y² dx + 8xy? dy)

A: In this question we will use basic of calculus i.e concept of integration. We will use green's…

Q: f(x)% 3D tanh In(2x) is equivalent to

A:

Q: How would you choose u when evaluating x" cos ax dx using inteeration by parts?

A: Given integral is ∫xn cos ax dx

Q: Use Simpson's rule with n = 4 to approximate cos(x) dx 1

A:

Q: The approximation of I tanx dx using composite Simpson's rule with n=5 is: = None of the choices

A:

Q: Let 5 sin æ + 6 cos y = 6. dy dx d?y dx?

A: 5 sinx +6 cosy = 6  Differentiating w.r.t x,  5 cosx +6 (-siny) dy/dx = 0  dy/dx = 5cosx/(6siny)

Q: Find dy if g-s(tant). and t= CostX)

A: Given functions,  y = sin (tan t) t = cos (x) the derivative to find is, dydx = dydtdxdt

Q: -1 Suppose y = sin ¹x. Then y arcsin 1 Oy= sin a Or = siny Or=

A: Given that:- y= sin--1x. Then  Topic:- inverse trignometry

Q: Use trapezoidal with 3 level Romberg ( k=3) to evaluate 1 Пх - Пх* cos dx 4

A: The complete solutions are given below

Q: 1. If y=tanx, prove that y=2(y² +1)(3y² +1).

A:

Q: If Z= x³ +y* +(x sin y) + (y cos x), Find (Zxx+ Zyy=?)

A:

Q: 2- Find dy/dx for y = In(tan(2x2))

A:

Q: If Z= sinh () show that: *=+y==0

A: GivenZ=sinhyx

Q: If y = eex the y' - y" + exy' is equal to?

A: The given equation is y=eex

Q: I. Find dy/dx in the following: 3. Y= tan (1+sinx)

A:

Q: Prove: ex. a. ſ csch x = In b. S sech x = 2 Arctan(e*) + c

A: a).  ∫cschx dx=∫2ex-e-x dx=∫2ex-1ex dx=∫2exex2-1 dx Put, ex=t⇒ex=dtdx⇒ex dx=dt Therefore, ∫cschx…

Q: 8. y = In(2e-t sin t)

A:

Q: Use the trapezoidal rule withn = 5 to approximate 4 cos(x) -dx

A: To approximate : ∫14cosxxdx using Trapezoidal rule with n=5

Q: 2. Find the length of the curve: y = 2 In (sin (x)):sxS*

A:

Q: hD (Hint: E =eD and Sinh x: 2 Q3: Prove that 8 = 2Sinh %3D

A: We will prove the following result.

Q: I need solution to this problem.

A:

Q: Find for y = tan(x) dy dz2

A:

Q: 2. Show that the LT of sin(wt) is L sin(wt)] (s) where w is a positive constant.

A:

Q: 1 The approximation of dx by the composite Trapezoidal Rule with n= 2 is +4 O X-

A:

Q: In (6x) to x if y = sin (5e') dt.

A:

Q: (3) Let 4 = x²y² + x sin y, find 2 dy in terms of x and y; dx (4) Find the equation of the tangent…

A: For the given problem, there are two questions. But according to rules of Bartleby only the first…

Q: If y = (sin-' x)², show that (1 – 2*) dy dr? dy 2. dx

A:

Q: If y = V1-x² sinx, prove that (1–x²) +xy =1– x². dx

A: Given that :- y=1-x2sin-1x Prove that :- 1-x2dydx+xy=1-x2

Q: If y = x tan-x- In /1+ x² then ¬1x-In V1+ x² dy is dx

A:

Q: 1) If f(x)= tan(5x), find  f'(5)=??????

A: Since you have posted more than one question, we solve the first one for you. For the remaining…

Q: if p> 1, (diverges; if p <1. 0o dx Prove that f p- 1 хР 1 Hence evaluate: dx. x6

A:

Q: |1- x 2 arctan + arcsin(2x – 1) = Hint using f Odx = C

A:

Q: If y=tanx , prove that y```=2(y^2+1)(3y^2+1)

A:

Q: The linear approximation at x = 0 to sin(6x) is A + Bx where A is: Preview and where B is: Preview

A: First of all, consider the formula to find the linear approximation at any point a for function any…

Q: 6) Find most general antiderivative of the fxn ) f(2) = secx (secx +tane) Secx +tanx, = secx COS X

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Q: 2T COs x dx

A:

Q: ons z = sin y arn

A:

Q: B ) if y= sinh¬1x then prove that =

A: Given y = sinh-1(x)sinh(y) = x On differentiating both sides , we get sinh(y)' = (x)'(cosh(y))dydx…

Q: Q2: - If y = 3sec3t and x = etan3t prove that: - dy (In3)2 + dx y 2logy x %3D

A: we have ,  y=3sec3t and x=etan3t we have to prove that , dydx=(ln3)2·yx·logyx…

Q: how can i derive this equation in 3 D? *be aqy ay az at Əx

A: Taking heat in three dimensions (I) Net amount of heat conducted into dxdydz per unit time.…

Q: Let f(x,y) = tan 1(sinh (y) + 2020 cos - 'y) + 4xy Calculate

A:

Q: If u(x, y) = 2 tan-1 2 and v= In (x² + y?) , prove that: a2v = 0 дхду dx2

A:

Q: If y = √1 − x² sin¯¹x, prove that (1− x²) ¹ + xy = 1− x². dx

A: We can prove the given the result by differentiating the given function.

Q: 1. Prove: a. csch x In +c %3D b. sech x = 2 Arctan(e*) + c %3D

A: 1. (a). To prove: ∫cschx=lnex-1ex+1+C Proof: We know that, sinhx=ex-e-x2 The left hand side can be…

Q: Find dy/dx if y = In (tan(x).3$ec(x) + /sin (x³)

A: given,

Minimization

In mathematics, traditional optimization problems are typically expressed in terms of minimization. When we talk about minimizing or maximizing a function, we refer to the maximum and minimum possible values of that function. This can be expressed in terms of global or local range. The definition of minimization in the thesaurus is the process of reducing something to a small amount, value, or position. Minimization (noun) is an instance of belittling or disparagement.

Maxima and Minima

The extreme points of a function are the maximum and the minimum points of the function. A maximum is attained when the function takes the maximum value and a minimum is attained when the function takes the minimum value.

Derivatives

A derivative means a change. Geometrically it can be represented as a line with some steepness. Imagine climbing a mountain which is very steep and 500 meters high. Is it easier to climb? Definitely not! Suppose walking on the road for 500 meters. Which one would be easier? Walking on the road would be much easier than climbing a mountain.  

Concavity

In calculus, concavity is a descriptor of mathematics that tells about the shape of the graph. It is the parameter that helps to estimate the maximum and minimum value of any of the functions and the concave nature using the graphical method. We use the first derivative test and second derivative test to understand the concave behavior of the function.