Find b, if the function f(x) = x². a) 1 b) -1 c) 0 d) 2

Q: suppos e fx(x)= 22 , o<x<77, and y = sinz . find fyld) and Fyl4) -

A: As per the question, we are given a probability distribution function (PDF) as : fx(x) = 2x/π2  for…

Q: Consider the two quadrature rules 0 Which one is better? Þƒ (¹) +cf (1), 2 3 + ߃ ( ¹² ) + yf าร์ (…

A: The function f(x) is integrated from 0 to 1.

Q: . Use the definition of error function, prove that [²' ( ²² ) = √T z

A: On solving this we will get

Q: Suppose that f(r, y) = 3x y + 8a? + 4y? then find the discriminant of f.

A: f(x,y) = 3x²y² + 8x² + 4y² So, fx = 6xy² + 16x  &amp;, fy = 6x²y + 8y  &amp;, fxx = 6y² + 16 &amp;,…

Q: Find the values of the constants a, b, c so that F = (axy + bz*)i+ (3x² – cz)j + (3xz? – y)k Is…

A:

Q: For the function f(x,y,z) = In (5x + 4y + 9z), find f,, fy, and f,.

A:

Q: If f(x,y)=x²y+y sin x, Prove that дхду дудх

A:

Q: ar to 2x -By + 2 =

A: we have to determine such that 3x + 2y – 7 = 0 is perpendicular to 2x -By + 2 = 0.

Q: Find the linear approximation at x=0  to 1/[sqrt(3-x)] . Write your answer in the form y = Ax+B .

A: Find the derivative of function at x =0

Q: Let f(x,y) = ax + by2 af where a and b are constants. If of at x = 1 and %3D ху y 2, then the…

A: Introduction :

Q: Use the convolution theorem to obtain f(t) if : 3.1) F'{F(jw)} = %3D 7+ 8iw-w?

A: Note: Here, we shall find  F-1Fjω=F-167+8iω-ω2=ft using the convolution theorem. (∵If…

Q: Given the multiple variable function f(x, y, z)= Ax*e» - Bz cosx*y°)+Cx*y*z?, where the coefficients…

A:

Q: Find f, and f, for f(x, y) = 10(9x – 8y+ 12)°. fx(Xx.y) = f,(x.y) D

A:

Q: Find f, and f, for f(x, y) = 12(6x-3y +8)°. %3D 1,(x.y) = %3D

A:

Q: Find the values of the constants a, b, c so that F = (axy + bz3)i+ (3x² – cz)j + (3xz? – y)k Is…

A: A vector F→ is said to be irrational if and only if cure F→ =0 i.e∆ x F→ = 0Given F→ = (axy+bz3) i^…

Q: f. . Prove false by creating a counterexample: 9(AUB) C P(A) U P(B)

A:

Q: Let f(x ,y, z) = x²yª + z³ and x = 4s?, y = 2st?, and z = 3s?t. %3D %3D

A:

Q: Prove that : V.(V×A)=0

A:

Q: Verify the statement is incorrect by giving a counterexample. X is greater than and equal to 5

A:

Q: Given that f(r, v) = xain v, determine fy(z, y).

A:

Q: Given f(x, y) = 4x³y², evaluate f(1,y) and fy(x,2).

A: We are given a function: f(x,y) = 4 x3y2 We need to find the partial derivative of the given…

Q: Find the linear approximation at x=0 to 1/(sqrt(2-x). Write your answer in the form y=Ax+B.

A:

Q: Use L and L to solue y' t 3y= f4) y)=5, where f4), (32)

A:

Q: Explain why, if a function u satisfies theequation, then it also satisfies the equation u'(x) +…

A: Concept: The calculus helps in understanding the changes between values that are related by a…

Q: If f(r, y) = (3r" + 21 – 12)', then fy is given by : %3D

A:

Q: Verify that the statement is incorrect by giving a counterexample. |x| is greater than or equals to…

A: Given- x≥5 To give- A counterexample to disprove the given statement. Concept Used- The modulus…

Q: Let f (x,y) = e**ytan (x + y), find дудх

A: Explanation of the solution is given below...

Q: If f(x, y) = (2x? + 8y²)í, then f_(0, 0) = %3D A) 0 В) 1 C) 4 D) 2 E) Does not exist

A:

Q: The range of f(x,y) = 2 - x2 + 4y² is : O [0,2] O xy-plane Joo+7] O

A:

Q: Write a in the form a = arT + aN N at t-0 for R(t) = t2i + %3D (t+r) + ( -r°*

A:

Q: show that T = 1/sqrt(x2 + y2) satisfies the equation Txx + Tyy = T 3.

A:

Q: EXERCISE 4.11.2 ONLY DO (D-F)****

A: For part d: According to the given information it is required to prove that for any positive integer…

Q: f(«, у, 2) — sec (9г + 3уг) fa = | fy = f: = ||

A:

Q: Show that u(x,t)= f((x+a*t)+f(x-a*t))/2

A: Given PDE is utt=a2uxx subject to ux,0=fxutx,0=0 We know that the general solution of the PDE is…

Q: Assume that ƒ′(3) = -1, g′(2) = 5, g(2) = 3, and y = ƒ(g(x)). What is y′ at x = 2?

A: Given:

Q: 2. Show that the function u = p(ry) + /TY p(y/x) provides the equation ‚Pu dy² y² = 0. %3D

A:

Q: 4. Now, determine the value of c in (0,1) such that f'(c) = 2 %3D fx) =4x

A:

Q: Find those constants a, b, c, d such that f(z) = ax² + bxy + y² + i(x² + cxy + dy?)

A: The given function is : fz=ax2+bxy+y2+i(x2+cxy+dy2)

Q: g(x) = Af(Bx), where: %3D A = %3D B =

A:

Q: What is the degree of f (x, y) = 2y + Væ² + y? ? O 1 O 2 O 1/2

A: We can solve as follows

Q: Find f, and f, for f(x, y) = 11(2x – 6y + 5)*. fx (x.y) =D

A:

Q: What is the degree of f(x, y) = 2y + √x² + y² ? 01 00 O 1/2

A: what is the degree of f(x,y)=2y+x2+y2 degree: it is the highest power of function

Q: Given that f(r, y) = }2 - - . (a) Calculate: f,, (b) Calculate: f„, (c) Are they equal?

A:

Q: Given f(x, y, z) = 6x2 + 2y? + 3z², find

A: Given,          fx,y,z=6x2+2y2+3z2

Q: Let (-) - {. S 8x², x 9 Find the values of a and b so that f will be differentiable at x = 9. а i b…

A: For differentiable function, left hand derivative is equal to right hand derivative

Q: f(z) =z? is discontinuous

A: f(z)= z2 is a polynomial function in z and polynomials are continuous everywhere.

Numerical Integration

In a mathematical investigation, numerical integration comprises a wide group of calculations for computing the mathematical estimation of definite integral, and likewise, the term is moreover in some cases used to depict the numerical solution of differential equations. The most important aspect of this theory is error analysis.