Home work 1- EXPlain the following i'nterVals on the line nuwbrs (a) -3 < X S (6) 38

Q: 2. Consider the surface f(x, y) = x² + y² = x² + 2xy - y² - a) Find all critical points of f (Hint,…

A: As we know a saddle point or minimax point is a point on the surface of the graph of a function…

Q: SOWE NING VARIATION OF PARAMETERS OR REDNOTON OF ORDER (D´+1) y = secx csc x

A:

Q: Find the area of the region under the curve y = 6 - 4x2 and above the x-axis

A: We’ll answer the first question since the exact one wasn’t specified. Please submit a new question…

Q: 1. find the linear approximation to /(x) at x = Xg. Use the linear approximation to estimate the…

A: Linear approximation

Q: 1- Fird the extreme va lues of the funetion and where the inter val S on whi'ch de eveensing and…

A: As per our company guidelines we are supposed to answer only first three sub-parts. Kindly repost…

Q: Let F(x) = J Ar) dt where the graph of Ax) is above (the graph consists of lines and a quarter…

A:

Q: 25+x + . Step 4 To find the least time differentiate T(x) with respect to x, T'(x)=- 3(2/25+x)…

A:

Q: 2 Estimate the minimum number of subintervals to approximate the value of| (4x² + 4) dx with an…

A: We will solve both these parts using basics of numerical analysis.

Q: 3 Using The humayenous Methal $ solue the DE : x Clay-lax) dy =y(ialony - lu x)dx

A:

Q: 1 Use Taylor's formula for f(x,y) at the origin to find quadratic and cubic approximations of f(x,y)…

A: Given: f(x,y)=11-2y-y    at (0,0)

Q: 2. An area is bounded by the curve y = 8/(x² + 4), the x-axis, and the lines x + 2 = 0 and x-2 = 0.…

A: Given, The curve bounded by y =  8/(x2+4) and x axis (y=0) And lines x+2=0 and x-2=0 x= -2 and x=2

Q: z4 + z? [()] Find and classify the isolated singularities and zeros of f(z) %3D 24-1

A:

Q: hat is the area of the region bounded by the line x = 4 and the curve x³ = x² + 2xy - y² = 0. ht:…

A:

Q: Find L(x). 2y x 3t %3D y + a' = 3e-t x (0) = y (0) = 0 3s2 L (x) = - (s+1)(s-2)(s²+1) 3(s-1) L (x) =…

A:

Q: 2. Determine the area of the region bounded by the curve y = x³ - x² - 2x, and a. the x-axis the…

A:

Q: ne particular solution is/are ocated at x = . Choose only one of them if here are 2 or more…

A:

Q: 3. Consider the function for r +0 f(r) = 1 %3D for r = 0. (b) Divide the interval [-1,1] into 2n…

A: given function is                                            f(x)=1x;  for x≠01 ;  for x=0 we have…

Q: Q1/ N Use the Trapezoidal rule to estimate the value of f(x) -2x sin'x in the interval x-0 to X-x…

A: A)f(x) = 2x sin2xfrom x = 0 to x = πwith n = 5Trapezoidal Rule∫ab f(x)dx = ∆x2 (f(xo) + 2f(x1) +…

Q: I. Evaluate the following. You are NOT allowed to use L’Hopital's rule. Vx² – 2x – 3x 3 - V11+ 4x 2x…

A:

Q: 4. Find the absolute extrema of the function f(x, y) = ry-x-3y on the triangular region with…

A: To find the absolute extrema of the function f(x,y).

Q: Q1. Obtain the Taylors linear approximation to the function f (x, y) = 2 x2 – x y + y2 +3x - 4 y +…

A:

Q: New tons method with al approximation ito find x,, the znd roximation to the root re equation x4…

A:

Q: te QY1. Show your work in the Sketch area to t. QY1 Use Gauss's technique to find the sum of the…

A:

Q: 6. Using the trapezoidal rule with three ordinates an estimate of the area under the curve y = sinx…

A: As per our guidelines, we are allowed to answer only one question. Since, you have asked multiple…

Q: J140-17 secC Maximum and Mininmum Valves of y = / On the interdal [o, 1 f min= manz

A:

Q: Q4A) Find area bounded by y = 0, y = 1-x²,x= 0 and x = 1. B)Is w=zx¹ analytical function or not? 2 2…

A:

Q: HWI Estimate the area unden y = sin (x) between x=0 and x= TJ with error 6.0005 Hw2|Estimate the…

A: with error ,area=2+0.0005

Q: e4x - 1 (a) lim x 0 COS x sin x (b) lim x0 et In x (c) lim x→1 x - 1

A:

Q: (b) We wish to evaluate the integral S1 exp(-x) dx using Gauss quadrature (based on Legendre…

A:

Q: (a) Suppose f"(x) = 0, what can you say about f (x)? Write it in general form. (b) Find the area of…

A: .

Q: (a) Find the critical point of f(x, y) = (4x2 y) (x² + 4y). (x,y)%3D (b) Find the discriminant, D(x,…

A: f(x, y) = 4x2-yx2+4y

Q: 2. a) Graph and shade the region bounded by y= cosx and y =-1 on [4, 7]. b) Find the area of the…

A: We will solve the following. The highlighted area (in red) is the shaded region.

Q: Consider the function f(z,y) = kr?- 2ry +y?. %3D 1. Show that (0, 0) is a critical point of f(z, y).…

A:

Q: J(X) = -3|X – 5| + 2 1. Why does J(X) have a critical point at X = 5? Explain. 2. Why does J(X)…

A:

Q: pifferentiate: y= 8 cos (16z*) DV = 512z sin(16z*) %3D OV = 512a' tan (16z) %3D O y' = -512' cot…

A: Solve for the derivative

Q: 1. The graph of f (x) = 8-x3 and line /which is tangent to f at x = 1 is shown in the figure to the…

A: Since you have asked a multi subpart question as per Bartleby's guidelines I will solve only first 3…

Q: 1) Calculate the area (A) of the limit domain by the equation curve y=1/x, x=(n-1), x=(x+1) and the…

A:

Q: 2. lim (x,y, Z)-) (0,0,0) EYaluate ベtyナスス

A: If limit depends upon the directions then limit does not exist.

Q: 2. Using the method of Lagrange multiplier, evaluate the max and min of the function: f (x, y) =xy…

A:

Q: 17. Region bounded by y = cos x, x = 0, x = and the x-a 4 %3D Rotate about: (a) the x-axis (c) y =…

A:

Q: 3. Consider the function for x +0 f(x) %3D for r = 0. (b) Divide the interval [-1, 1] into 2n parts.…

A: using trapezoidal rule

Q: II1. True or False (no reasons necessary) If Vf(a, b) = 0, then f (x, y) definitely has a local…

A:

Q: Using the definition of integral12. x^2 dx as a limit of a sum of rectangles, compute integral12.…

A: Given ∫12x2dx

Q: The area between the curves y = 3 cos (z) + 3 and y = -3 cos (r) on the interval (0, n) is: -T+6/3…

A: We need to determine the area enclosed by both curves. If fx&gt;g(x) in an interval a, b, then the…

Q: The area of the region bounded by the parabola y = 1 – x², the x-axis and the lines x = -2, x = 1 is…

A: Find the area of the region.

Q: Create a unique aNadratic furncbion in vertex form Ehat mects the following criteria: - hos an aris…

A: Given: For quadratic equation  the axis of symmetry x=-5 minimum of y=-9 wider than the quadratic…

Q: on Find the absolute minimum and maximum of the function f(x, y) = 2x¹ - xy² + 2y² the region 0≤x≤…

A:

Q: 1 2 1. Find the area bounded by the curve y =x² + 5, the x-axis, and the vertical lines x = 2 and x…

A:

Q: 1- x Find the area of the region between the curve y = 2- 0 < x < 1, and the x-axis. p2 1 1'

A: here we have ................x-axis ................given interval

Equations and Inequations

Equations and inequalities describe the relationship between two mathematical expressions.

Linear Functions

A linear function can just be a constant, or it can be the constant multiplied with the variable like x or y. If the variables are of the form, x2, x1/2 or y2 it is not linear. The exponent over the variables should always be 1.