Differentiate f(x)= (cot(x2))/x3

Q: Find the volume of a parallelepiped if four of its eight vertices are P(0,0, 0), Q(3, 4, 0), R(0, –3...

A: Let, P, Q, R, S be the four vertices of a parallelepiped. Then, we find the vectors, a=PQb=PRc=PS Th...

Q: Find the domain and range of f, Also graph the function

A: Given function is fx=1x2. To find the domain and range of the function and graph the function. Solut...

Q: act answer or roune

A: The function given is, fx. The relation of function inverse is, f'-11=1f'f-1xf'f-1x·f'-11=1. The slo...

Q: For the described curve, decide if the curve would be more easily given by a polar equation or a car...

A: The standard equation of a circle in the cartesian form with the center at the origin is given by th...

Q: Find all of the first order partial derivatives for the following function

A: Derivatives can be defined as rate of change of function with respect to an independent variable. It...

Q: In(æ) Differentiate:

A: Derivatives can be defined as rate of change of function with respect to an independent variable. It...

Q: x cos x Y = sin* cOS x find d dx | sin-

A: To  find: dydx=?

Q: By squeeze theorem, the sequence an= is n2 converges to, OA. 0 OB.1 Ов. Oc. D.

A: The given sequence lies between limn→∞cos-πn2 and limn→∞cosπn2.

Q: Kindly show detailed solution. x2 Maximum point of y2 х-2

A: Given a function : y2=x2x-2 We need to find the maximum point. Let's begin.

Q: onsider the vector function r(t) = (5t, 3, t). Find the unit tangent vector T(t) when t= 1.

A:

Q: 13x +5 If x- 2x dx = A In|x

A: Given that, ∫13x+5x2-2xdx=Alnx+Blnx-2+C We have to find the value of A + B.

Q: Find the following F(s) = t² e=st dt s > 0

A: The Laplace transform of a function ft is given by Fs=Lft=∫0∞fte-stdt, where Fs is a Laplace transfo...

Q: In differential equations, solve the following:

A: Volume =13πr2h              =13×π×4×8=32π834 th of volume spelled out =8π 

Q: FG)= St SnA AS Crtrial purnts and at the 1.E va luate endponts of the gruen inteval Iden tfn (ocal a...

A: Given: f(x)=x+sin x  (0≤x≤2π)To find the critical points, endpoints, local/global maxima and minima ...

Q: Find parametric equations for the path of a particle that moves along the circle x2 + (y − 3)2 = 16 ...

A: A circle defined parametrically takes the form: x=r cos(t)+h y=r sin(t) +k

Q: 5) Find the following of the function f(x,y) =xy+cos y+ysin x

A: To find: The partial derivatives ∂2f∂x2,∂2f∂y2,∂2f∂x∂y. Given: The function is fx,y=x2y+cosy+ysinx. ...

Q: find a cartesian equation for the curve r2cos(2θ)=1

A: r2cos2θ=1

Q: Please evaluate dy/dx

A: To find dy/dx: 10.y = arc cot ( sinh3x ) dy/dx = [1/(1+sinh23x) ]( cosh3x) 3  = (3 cosh3x) / (1+sinh...

Q: Solve the following equation for x. (e5)*• e In 1 = 11 x= (Type an exact answer.)

A: e5x.eln 1=11

Q: Determine whether the sequence whose nth term is n+1 is increasing or decreasing? n+3 an OA Increasi...

A: Given: an=n+1n+3 We know that any given functiony=fx is increasing if f'x>0 and decreasing if f'x...

Q: Which of the following methods cannot be used to solve for side b n the diagram below? Sine Law Cosi...

A: We have to find that which of the given methods can be used to find the side 'b' in the following fi...

Q: Match conic section with one of these equations: x2/4 + y2/9 = 1, x2/2 + y2 = 1, y2/4 - x2 = 1, x2/4...

A: Given a figure and four equations as follows ;  x24 + y29 = 1        [Equation 1]x22 + y2 = 1       ...

Q: :Please evaluate this integral:

A: One of the two main parts of calculus which are concerned with the study of integrals, as opposed to...

Q: Eliminate the parameter to find a cartesian equation of the curve x = t4, y = ln(t)

A: A function is a relation which maps each value in its domain to exactly one value in its range. A cu...

Q: CALCULATING WORK

A:

Q: Complete the square and find the indefinite integral.

A: To find: The integral of ∫x22x-x2dx Formula used: Power rule of integration: ∫xndx=xn+1n+1 sin2u=121...

Q: Solve the following equation for x. 4 ex/11 - 5 = 0 x=0 X =

A: We have given equation  4 ex/11 -5=0 4ex/11=5 ex/11=54 Taking natural log both side lnex/11 =ln54 x1...

Q: Write each angle measure in degree-minute-second (DMS) form.  56.875 degrees

A: To write each angle measure in degree-minute-second (DMS) form.

Q: Fined derivative for the following function by use Rule 5 & Rule 6:- (x – 1)(x² y – 2x) .4

A: To find the derivative of the function: y=x-1x2-2xx4 Solution: Product rule of differentiation state...

Q: CALCULATING WORK

A: Given:  Weight w=500-lb Length L=300 ft

Q: Given SV-x* + 4x + 5 dx. Using trigonometric substitution, what is the integral form in terms of 8? ...

A: Trigonometric identities: sin2θ+cos2θ=1cos2θ=1+cos2θ2 If an expression is x2+bx, then we need to add...

Q: Match column A with column B Evaluate the following: So² Sx?x+1 x dy dx 4/3 So' SxX x dy dx Choose. ...

A: Solution:GivenTo evaluate the followingFormula:∫xndx=xn+1n+1+C  

Q: a. How fast is the surface area of a cube changing when the edge is 30 cm. If the edge is changing a...

A: Given: a=30cm, dadt=3 mmsec We know that surface areaS.A. of a cube is given by S.A.=6a2            ...

Q: Please evaluate dy/dx

A: Since you have posted multiple questions, as per our policy we will answer first question. Please re...

Q: The university doctor asked me to solve the question indicated by the arrow in the picture without t...

A: Given,y=x-1x2-2xx4y=x3-2x2-x2+2xx4y=x3-3x2+2xx4y=xxx2-3x+2x3y=x2-3x+2x3differntiating both sides w.r...

Q: Use L’Hospital’s Rule to evaluate the given limit

A: we have to use L' Hospitals' Rule to evaluate the limit.  limx→1+xx-1-xlnx

Q: help me please

A: 7)  Surface Area of cylinder=2πr2+2πrh Volume of cylinder=280 cm3   V=πr2h=280 cm3 πr2h=280  h=280πr...

Q: find the volume of the solid that results when the region enclosed by the curves y=(9-(x^2),y=0)

A: To find: The volume of solid generated by curves y=9-x2, y=0 Formula used: The volume of solid gener...

Q: The two lines graphed on the coordinate grid each represent an equation. 6- 4 2 -6 -2 6 2 What is th...

A: The two lines graphed on the coordinate grid represents an equation.we have to find the ordered pair...

Q: Solve the IVP for y(1) = ?

A: Given,dydt=13.1y-13.94y2113.1y-13.94y2dy=dt1y13.1-13.94ydy=dtintegrating both the sides,∫1y13.1-13.9...

Q: x+1

A: An improper integral is a definite integral that has either or both limits infinite. In other words,...

Q: x ty S'SL" (x+y +z) dz dy dx

A:   To evaluate ∫01∫0x∫0x + y x + y + z dz dy dx

Q: Arrange the following equations in linear form ( + P(x)y = Q(x)) and identify the P(x) and the Integ...

A:

Q: Let f(x) = V3x2 + 3x + 3 f' (æ) = f'(5) : %3|

A: The differentiation of the nested form of functions can be done by using the chain rule. According t...

Q: Kindly answer this

A:   To find the volume of the solid capped by the surface z = 1 - y - x2 over the region bounded on th...

Q: Let F(x) be antiderivative of f(x). Find F(8) given that | f(x) dæ = 2 f(x) dx, | f(x) dx = –3 and F...

A: Integration is the process of finding the anti-derivative function of the given function. The integr...

Q: The figure below shows a solid made from stacks of cubes. The answer box shows the same solid viewed...

A: From the figure,number of cubes on at front =3+2+1=6number of cubes on at back=3+3+2=8

Q: If 3xy+x^2=7 and dy/dt=-16, find dx/dt when x=1

A: Derivative, in mathematics the rate of change of a function with respect to a variable. Derivatives ...

Q: Use a table of integrals to find the indefinite integral.

A: To find: The integration of ∫e3x1+ex3dx. Formula used: Power rule of integration: ∫xndx=xn+1n+1+C ∫1...

Q: Calculus Question

A:     Given, Vertical side of tank is given. The weight density of water=62.4 pounds per cubic fee...

Transformation of Graphs

The word ‘transformation’ means modification. Transformation of the graph of a function is a process by which we modify or change the original graph and make a new graph.

Exponential Functions

The exponential function is a type of mathematical function which is used in real-world contexts. It helps to find out the exponential decay model or exponential growth model, in mathematical models. In this topic, we will understand descriptive rules, concepts, structures, graphs, interpreter series, work formulas, and examples of functions involving exponents.