s continuous on la,b), then d f(x)dx = f(x) dx A) True B) False

Q: (a) Use the trapezoidal rule to approximate the integral. dx

A: Solution of given question is written in below steps.

Q: The linear approximation at æ = 0 to sin(2z) is A + Bx where A is:| Previev and where B is: |…

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Q: 3 Estimate the integral 1 dx by the trapezoidal rule using n = 4. + 1 Vx3

A: ∫abf(x)dx≈Δx(f(x0)+f(x1)2+f(x1)+f(x2)2+f(x2)+f(x3)2+⋯+ f(xn−1)+f(xn)2) where ∆x =b -an

Q: Integrate sin 6y sec 3y dy from limit 0 to π

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Q: Integrate the following function by using trapezoidal rule. 142*dx

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Q: What is frz, fyy, and fyz of f(x, y) = In(y²")?

A: Given:           f(x,y)=lnyx2          fx=∂∂xlnyx2         Treating y as constant variable…

Q: express the limit as a derivative.

A: Given limit is: The limit definition of a derivative is given by:

Q: sen z + cos x dz | (tag z + 1) dx = In sec x+z + C 37. %3D cos 2

A: 37.   Given integral, ∫sen x+ cos xcos xdx

Q: Evaluate f S S," x dz dy dx

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Q: Suppose f(x) = df Find the derivative dx In(In(In(In(x)))). f' (x) :

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Q: 2. dx Ix Also, Prove that 22 %3D dxdj = dy dX

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Q: The error is numerically computing the integral | 1 dx using the +4 trapezoidal rule with two…

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Q: If f = 5x2y2 - XY2 then find af at (3,1) %3D dx

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Q: In integrating the function fxIn Sx dr using integration by parts, what would be your du? du = In 5x…

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Q: What is the value of the integral ∫2−2 max [1,x2] dx ?

A: This question is related to integration.

Q: he derivative of f(x,y)=10x^y at (e,1) in the direction of v = is

A: From the expression of the directional derivative:   D.D=∇fpx,y,z·a→a→   Given:…

Q: What is the total change of f(x) if f'(x)= sin(x) from [0, π]? A/

A: Answer: As per guidelines , we can do 1 question at one time , so please post other question…

Q: 4) Use integration by parts to find f x² In 5x dx

A: As per our guidelines we need to solve only one question.please, repost the remaining questions as…

Q: B) prove du d 1. sec u = secu tan u %3D dx dx

A: Since the student has posted multiple questions and does not mention any specific question, so we…

Q: Use integration by parts to prove the reductionformula.

A: Consider the following integration by parts formula: ∫uvdx=u∫vdx-∫dudx∫vdxdx ILATE Rule: We have two…

Q: Express the limit as a derivative.

A: Given, limθ→πcos θ-sin θ+1θ-π

Q: / f'(x) sin x dx = 8, / f(x) cos x dx?

A:

Q: What value for a will make sinx { ,X # 0 2x f(x) = %3D 3D ,X = 0 a continuous function?

A: For a function f(x) to be continuous at x = a,limx→a-f(x) = limx→a+f(x) = f(a)

Q: Express the limit as a derivative.

A: Our Aim is to evaluate the limit of the expression given below:-limt→πsin (t) cos (t)t-π-(i)

Q: n(x)=3x?4k+1 %3D

A:

Q: dy/dx = sec(x)tan(x)

A: Given: dydx=sec(x) tan(x) if y=sec(x) tan(x)

Q: d sec z = sec z tan z dz

A: The function is a rule that associates or fixes a number to the particular point z . If , then the…

Q: Evaluate 2Sin x´dx, by (i) mid-point rule, and (ii) Simpson's 1/3 rule.

A: i)Given:        ∫242sinx2dx   Mid-point rule:       ∫abf(x)dx=∆xfx0+x12+fx1+x22+fx2+x32+...…

Q: dy Find by implicit differentiation. dz 3+ 5z = sin(ry) dy

A: We can find the answer using implicit differentiation as below.

Q: Ex. 2. Prove thät if two equal and perfectly elastic balls moving in the same direction collide…

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Q: Use the trapezium rule to find [2" dx taking ordinates with interval 0.25, in three decimal places.

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Q: 4. Use the definition of integration to find (1+2x' ) dx , that is find lim f(x; )Ax

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Q: What are the new limits of integration if apply the substitution u = 7x + a to the integral sin (7x…

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Q: The derivative of sec(e) is tanx O 1) tan(e*") sec{e*™) O 2) tan(e**) sec(e*)x e** 3) tan(e)…

A: topic - derivative of a function

Q: If f has a continuous second derivative on [a, b], then the error E in approximating f(x) dx by the…

A: (a) Trapezoidal Rule. First we need to find the maximum of f''x. In the problem given, fx=7x.…

Q: we have to check the DE sin(x) +y cos(x) = 1 for Exact then My= dx None of These - sin(x) sin(x)…

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Q: dy by implicit differentiatio Find

A: According to the question, we have the the equation,x7y-xy7=8we have to find dydx so,

Q: Use the Trapezoidal Rule with n = 4 to estimate f, (x³ + 1)dx.

A: We have to estimate ∫-11x3+1dx by using the Trapezoidal rule with n = 4.

Q: Show that the function f(z) = sin x cosh y + i cos x sinh y is continuous as well as analytic every…

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Q: Assuming that x> 0, use differentiation to justify the formula dx = In x +C. %3D d dx = In |x| + C,…

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

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Q: What is the value of the integral ∫2−2 max[1,x2]dx ?

A: Value of the given integral is 2x [1- ((x^2) /3) ]

Q: ntegrate dx/sqrt(E-((kx^2)/2)) ;    E,k = const.

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Q: Use the First Fundamental Theorem of Calculus to find F"(x) if = [*_ sinh√/1 +ť² dt. F(x) =

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Q: Show that the function f(z)=sin x cosh y+i cosx sinh y is continious as well as analytic every…

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Q: The minimum value of n required to approximate xe dx by composite Trapezoidal rule with an error…

A: Find the minimum value of n required to approximate ∫02xe-xdx by composite Trapezoidal rule with and…

Q: er dy %3D sec da

A: The given differential equation is exdydx=sec y and the initial condition is y0=1. Solve the given…

Q: O Use integration by part ax Cosbx dx

A:

Q: Show that the function f(z)=sin x coshy+I cosx sinh y  is continuous as well as analytic every where

A: