Differentiate the following functions using product rule. 1. f (æ) = (3x – 9) (x – 6) 2. ƒ (x) = (æ³ – 2æ² + – 6) (2æ² – 2æ + 4) - -- -

Q: Determine whether the function t(xry, 2)=x' +y-2 (where Y,/ and Ź are s tritly greater than 0) is…

A: Use Hessian matrix

Q: B) Estimate the next root of the function f(x)=x^3-x-1 using Muller method, let x0=1, x1=2, x2=1.5

A: Muller method: The Muller approach is applicable to any root-finding programme, but it is especially…

Q: Consider the piecewise-defined function f defined by 8 -3x2 11 6x { if x 1 if x 1 f(x) Find f'(1).…

A: Given,

Q: 27. Sketch the following functions 1 a) y = -(2x – 1)(x +1)(4 + x)(x – 5) g(x) = %3D b) x² - 4x – 21…

A: The graph of a function f(x) is a set of ordered pair of x and y, such that y=f(x) for every point x…

Q: Let f(x)= x2 − 6. Prove that the root of this function is equal to √6 {correct to 2 dp}, and lays…

A:

Q: Find the most general antiderivatives of the following functions. ƒ(x) = x² + 2x + 3

A: GIVEN: f(x) = x2 + 2x + 3

Q: Verify the Rolle's theorem for the function (x² – 1)(x – 2) on [-1,2] Find the point in the interval…

A: We can use application of derivative in order to solve the given problem.

Q: of and ду of For the function f(x,y) = In (x+ 3y), find

A:

Q: 1. Test the continuity of the following functions at given points? x² -1 -1 <x<0 2x 0 <x<1 (a) fx)=…

A:

Q: Find the particular antiderivative F(x) of f(x) = 18x – 11 that satisfies F(1) . 8.

A: Given function , f(x)=18-x

Q: Find the linearization L(x)  of the function f(x) = x^4 -2x^2+3  at  x =0.

A:

Q: Find f(1) if f(t) dt = x- x + 2x2- 2, x >1. %3D

A: Given, ∫1x2ftdt = x6 -x4  +2x2 -2               x≥1 We have to find   f1

Q: f(x,y) = -x4 +2x2y - 1/2y2-4y +12

A: To find the relative extrema of the following function.

Q: Consider the following function. H(x, y) = In(8x² + 3y²) (a) Find fxx(2,3). (b) Find fyy(2,3). (c)…

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Q: Verify the Rolle's Theorem for the function (x2 – 1)(x – 2) on [-1,2] find the point in the interval…

A:

Q: {(u)= (u² -3)*

A: Given the function is  f(u) = 12u2-32. We have to find f'(u).

Q: Calculate L3, R3, and M3 for the following function over the interval [0,3]. f(x) = Vx + 1

A: The given function f(x)=x+1 over the interval [0,3]

Q: . Suppose that f(r) is a function given by for 0<r<7, f(z) = for -n <I<0.

A:

Q: Determine the c which satisfy the conclusion of Rolle’s Theorem for the given function and interval.…

A:

Q: Vhich of the following is NOT TRUE about the function f(x, y) = e² + e"?

A:

Q: Inlegrate the function f(x,9) -x,3zy over the rectungle R: e6x41 and sy61

A:

Q: find the domain of the following function and show it in the xy plane. 1. f(x, y) = In(9 – x² – y?)…

A: Let's find.

Q: Find the particular antiderivative F(x) of f(x)=4x−3 that satisfies F(1)=8.

A: The given function f(x)=4x-3, its antiderivative satisfies F(1)=8

Q: of Find and for the following function. f(x,y) = e Y In (3y)

A:

Q: 3 B Consider the following function, z= x -2xyty't yn Lind the alues of ag Ddz,z,when redgyel dy 6.

A: Given : z = x2 -2xy + y3 + yw

Q: Find the most general antiderivative of the following function. f(x) = 2e" - 8x %3D

A: Given that a function f(x) = 2ex - 8x We find antiderivative of this function.we know that…

Q: Compute lim,0f (x) for each of the following functions f (x). 3x (c) f (x) = Vx2 + 8 3x (d) f (x) =…

A: topic - limits

Q: use implicit differentation to find the the dervivative of the following functions: a) x3+2y2=5…

A: Given: a) x3+2y2=5

Q: u² -v² +uv x=In", y=' (11–v)-

A: two functions x=lnuv...........(i) and y=u2-v2+uv(u-v)2..........(ii) are given. To find the…

Q: Let f(x)=4x^2-2x-2 find the following: 1) f(x+h)= 2) (f(x+h)-f(x))= 3) lim h→0 (f(x+h)−f(x))/h 4)…

A: We have to find 1) f(x+h)=2) (f(x+h)-f(x))=3) lim h→0 (f(x+h)−f(x))/h4) Find the equation of the…

Q: 1. Decide if there is an analytic function f (x + iy) whose real part satisfies Re(f) = xe".|

A: Given problem: To decide analytic function fx+iy whose real part satisfies Ref=xey.

Q: Compute the following values for the given function. f(x, y) = 4x2 + 2xy – 7x + 4 f(1, 2) %3D f(2,…

A:

Q: Find and sketch the domain of the function f (x, y) = In(9 – x² – 9y²).

A: The given function,  f(x,y)=ln9-x2-9y2

Q: Find the solution using homogenous function substitution of the following DE Show that 2xyy' == x² +…

A:

Q: Determine whether the following function is continuous at the given point z =: 3x2 + 14x – 5 1 3…

A: Given. The function fx=3x2+14x-53x-1  x≠13163x=13 We have to check the continuity of the function at…

Q: Since f(x) is continuous between a and b, the function needs to cross the x-axis. O TRUE O FALSE O…

A: Given fx is continuous between a and b

Q: Aen vity # 2 BLs auss ME! t) flx):1 Xスー 2.

A:

Q: consider a function f:lo 11-» R. and etheruoise iff RELmaan amntegrable DY not A=3+1

A:

Q: Consider the following. z = x2 + y2, x = 3s + 7t, y = s +t az az and as Find by using the chain…

A:

Q: 4. Are the following functions cubic splines? a. f(x) - x- 2x + 3, 0 sxs 1, - 2x - 3x2 + x + 2, 1 s…

A: Given :(a) f(x)=x3-2x+3, 0≤x≤1             =2x3-3x2+x+2, 1≤x≤2(b) f(x)=5x3-3x2+1 0≤x≤1…

Q: Algebraically show that each of the given combinations are equivalent to the given functions. If…

A: This question can be solved using the concept of multiplication of two algebraic function.

Q: Compute the following values for the given function. f(x, y) = 8xye(x2 + y2) f(0, 0) f(0, 1) f(1, 1)…

A:

Q: Consider the function f(x) = 12x' + 60x 100x + 6. f(z) has inflection points at (reading from left…

A: Here, f(x)=12x5+60x4-100x3+6

Q: Suppose that x = x(t) and y = y(t) are both functions of t. If 22 + y = 20, and -1 when x = 2 and y…

A: x2 + y2 = 20 Differentiate with respect to t 2x dx/dt + 2y dy/dt = 0 In this equation we put x = 2,…

Q: se the variable u for the inside function to express each of the following a (a) y = 910x-1 O u =…

A: Topic = Functions u=10x-1 , y=9u

Q: Let f(x, y) = -e2"-y + In(3x – y). Find the domain of this function.

A:

Q: Consider the following function f(x) = (2x + 3) e* Find the equation of the tan gent line to the…

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Q: Form the PDE by eliminating the arbitrary functions from the relation z = f(xy)

A:

Q: of Find of and for the following function. ду f(x.y) = x° – 2xy – 2y²

A:

Linear Algebra

In mathematics, problems can be solved by the arithmetic operators like addition, subtraction, multiplication, and division. In algebra, we represent the numbers by any letter called a variable. If these variables are of degree 1, then it is studied under linear algebra. The first-degree equations involving algebraic expressions are called linear equations. That is, if you represent it by drawing a graph you will get a straight line.