30. Find the continuous function f(t) satisfying csin z for all r. 2+ f(t)dt = sin2015 /3

Q: Find a function f € span(1, cos x, sin x) which minimizes the integral 2πT √²* |x +1 − f(x)| ²dx.

A: Given a function                     f∈span1, cosx, sinx

Q: That the value of the integration g(1) = 0, g(2) = 0 1-e) -dt where g is a function that is…

A:

Q: Which of the following is the partial derivative with respect to x of the function f(x, y) = 2y sin…

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Q: tinuous at t= 0, it is continuous at every other point. 3 If the autocorrelation function R(t) of a…

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Q: 02/Evaluate the integs al t'sec"t dt (tant-1)

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Q: Find General Solution on this Diffential E Qution by using (uC set) =e +Sin X

A: Given differential equation is y''+y'-2y=ex+sinxfind the general solution

Q: Suppose that f(x) has a continuous derivative, (T/2 f(-т/2) — 0, f(T/2) = T/4 and dx = 3. %3D 7/2…

A: Given that:

Q: Let z = cosh t. Find the differential dz when t = In 3 and dt = 0.2 O 4/3 O 4/15 O 8/15 O 1/3

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Q: Determine the first order partial derivative of the following: F(x, y) = cos(e^t) dt and…

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Q: (b) Compute the partial derivative fy at the point (x, y) = (1, 1), or show that it does not exist.…

A: Let f:R2→R  be the function   F(x,y)=x-1.y-113(b) compute the partial derivative fy at the point…

Q: Determine | An (x) An+1(x) dx, from the relation: tn .1 Σ (2n + 1)! tn+1 A, (x) An+1(x) dx n=0 n -1

A:

Q: 12.) Compute the first partial derivatives of the following function. f(x,y) = 2- tan 1 (7x² + 2y²)…

A: The given function isf(x, y) =2tan-17x2+2y2to find partial derivative fx, fy

Q: Consider the function 0. f(t)3D- t = 0 if if t # 0

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Q: 1. Determine if the following improper integrals converges or diverges dx a. (1+r*)'/3 b. cos(x-1)…

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Q: Let y 5x²8x + 4. If Ax = 0.1 at x = 1, use = differentials to estimate Ay Ay ~

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Q: Find both first partial derivatives. z = sin 5x cos 5y

A: The given function is z=sin5x cos5y. Differentiate the above equation partially with respect to x as…

Q: 6. The improper integral 1 dx converges to Vx-5 4 2 попе 1

A:

Q: Use the bise ction to approximate the solution of F(X)=Vx - cos X = 0 accurate to within 10 -3 on…

A: Bisection method: In order to find root of equation f(x)=0 in a,b such that f(a)f(b)<0 Bisect the…

Q: 12. Show that F(x) = sinx – x cos x+2 is an antiderivative of f(x) = x sinx.

A: Given, F(x)=sinx-xcosx+2 To show that the above function is an antiderivative of f(x)=xsins.

Q: 8 Evaluate the integral dx using the two-point Gaussian quadrature rule. 16+z1 -2

A:

Q: Suppose that z = xy² and x and y are differentiable func- tions of t with x =2,y = when t = -1. Then…

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Q: Use at least two methods to prove that dr/dt=0 when r=√x2 + y2, x=α cos t, and y=α sin t if α is a…

A: First method   r=x2+y2r=(α cost)2+α sint2            since x=α cost and y=α sint  =α2cos2t+α2sin2t…

Q: Consider f(x) = sin(2x) + cos(4x), 0 ≤ x ≤ 1. Integrate f over the given interval of x, using…

A: Consider the provided question, fx=sin2x+cos4x, 0≤x≤1. We need to Integrate 'f' over the given…

Q: 2. Find the indefinite integral: S (Vã+ - x + - 1) dx 6 .3 X X

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Q: of Let f(x,y)=tanh-1(x-y) with x=e" and y= usinh (1). Then the value of Ot (u,t) =(4,In 2) is equal…

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Q: 11. The function f(x) is defined on [1, o0) and satisfies VTO dt. 10 Find f(x).

A:

Q: 60. Is there a value of b that will make Sx + b, x<0 (cos x, x20 continuous at x= 0? Differentiable…

A: A function is continuous at x=c, if LHL at c=f(c)=RHL at climx→c-f(x)=f(c)=limx→c+f(x) A function is…

Q: find the first partial derivatives of the function f(x, y) = integral from y to x of cos(t^2) dt

A: the given function is , f(x,y)= ∫xycos(t2)dt

Q: 1 The improper integral -dx is given by: x² +8x+41 Select one: O a. None of these sec-'((b+4)/5) de…

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Q: of Let f (x, y) = tanh-¹(x-y) with x=e" and y= usinh (t). Then the value of dt (u,t) =(4, In 2) is…

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Q: Suppose Fas satisfies f'cx) = fex). Prove that 3fx)sin(3x) + f'cx)cos (3x) Sfewcos(3x) dx = %3D 10

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Q: 2. Suppose that h(x) is a continuous function, h(-1/4) = 1/2, h(7/4) = 1 and h(2)dx = 2. Evaluate…

A: Here, given that h-π4=12, hπ4=1 &amp; ∫-11h(x)dx=2...(1)

Q: If the function f(x) is defined on the 2 intervallo, TT) and f'(x) = -cos X (sinx) than f(x) has…

A: Given that fx is a function defined on an interval 0,π whose derivative f'x=-cosx1+sinx2 To find the…

Q: 3. Prove by using the Squeeze Theorem, or otherwise: 1 t2 dt is continuous at 0. T sin t (a) (b) 1+…

A: Note: As per bartleby instruction when more then one question is given only one has to be answered.…

Q: If f(x, y, z) = 2 sin(100xy) In(2), compute the value of the limit f(1, h, e) – f(1,0, e) lim h→0 h

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Q: 1 The partial derivative of f(x, y, z) = Arctan with respect to z is xy? z³

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

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Q: Find all the second partial derivative T = e-4r cos(0) -4r, Trr 16e 'cos (0) %3D Tre = 4e -4r,…

A: “Since you have posted a question with multiple sub-parts, we will solve the first three subparts…

Q: Evaluate the integral: sinh 3x csch 3x dx coth 3x "+C 3 coth X +C 3 - coth x +C - 3 - coth 3x +C 3

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Q: Assume x and y are functions of t. Evaluate dy / dt for 4xey = 8 - ln 64 + 6ln x, with the…

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Q: 3. Estimate the integral v2 + x² dx using appropriate of Simpson's rule with step size, h = 0.2.

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Q: 32 2 f is continuous and | f(t) dt = 6, find the integral / t* f(t) dt.

A: Given problem:-

Q: What value of x > -1 maximizes the integral / t²(3 – t)dt?

A:

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: Use the second fundamental theorem of calculus along with the chain rule to find d sint dt dx 1 o…

A:

Q: Consider a Lorenz curve given by f(x)=x^n for 0≤x≤1 and n≥1. What happens to the Gini index G.I as…

A: Consider the given function. fx=xn The Gini index is defined as, GI=2∫abx-fxdx

Q: ди + 3x- = 1 + u, dx ди -co 0, dt u(x, 0) = f(x).

A:

Contingency Table

A contingency table can be defined as the visual representation of the relationship between two or more categorical variables that can be evaluated and registered. It is a categorical version of the scatterplot, which is used to investigate the linear relationship between two variables. A contingency table is indeed a type of frequency distribution table that displays two variables at the same time.

Binomial Distribution

Binomial is an algebraic expression of the sum or the difference of two terms. Before knowing about binomial distribution, we must know about the binomial theorem.