Which of the following statements is true? V2x+y-3 1 A (x.y) (4,1) 2x+y-9 lim %3D 6 6x2 lim =3 (x.y) - (0,0) 2x2 - xy+11y ху- 4у 1 lim (x,y) → (4,0) x2 -8x +y2 + 16 2 x5y D f(x) = x8+ x?y? ' (x,y) (0,0) D is continuous at (0,0). (x,y) = (0,0)

Q: 6. lim t+0o e3t + 4t

A: Given: limt→∞t2e3t+4t To determine: The value of the given limit.

Q: Consider the function P(x) = (x – 2)°(x – 6) - The y-intercept is the point (0,-24) The…

A: Recall: The x intercept is the point where the line crosses the x axis .At this point y=0. The y…

Q: Identify and sketch the domain of f(x, y) = y² + 4x + 2 In(1-x² - y²)

A:

Q: An + 1 ≤ n² for all integers n ≥ 5.

A: In this solution we will prove that 4n+1≤n2 for all integers n≥5 using principle of mathematical…

Q: 20x10 – 2x + 2 lim V 5x10 +x E- ;*+ or" ||

A: First we put the given value in the function if it attain a finite value then we achieved the answer…

Q: Find the maximal value of the function f(x,y)=2x3-y3 on the circle of equation x2+y2=7.

A: We have to find the maximal value of the function  on the circle of equation

Q: Determine a mapping of the form (x, y) (_) from y = f(x) for each of the following. y = 3f(2x)…

A:

Q: -22²-1y²+2x+9y Suppose that f(x, y) = then find the discriminant of f. e

A:

Q: Find f(x) and g(x) such that h(x) = (fog)(x). 4 h(x) = (6x+3)* Choose the correct pair of functions.…

A:

Q: Let f(x, y) = 2x - 4y + 7. Find the following. (a) f(3,-1) (b) f(-5, 1) (c) f(-5, -4) (d) f(0, 7)

A: Since you have posted multiple subparts, as per our policy we will answer first three subparts.…

Q: Decompose the function y=(4-2x3)4 in the form y=f(u) and u=g(x)   use g(x) = 4-2x3

A: Given function      y=4-2x34  then  we have  to decompose  the given  function  in the form  y=fu…

Q: 1. y=x√x²-2

A: Note: According to our policy, we can answer only the first question or the first three subparts of…

Q: Use the given graph of y = f(x) to graph the function g : g(x) = 1/2f(2x)

A: Using the given graph of y=f(x) : We are to graph the function g: gx=12f(2x)

Q: Find the linear function f(x) passing through (6,8) and (8,10) Enter answer in form…

A: Explanation of the answer is as follows

Q: Find and sketch the domain for the function

A:

Q: 5. Trace the curve: r = 4 cos 0 e (degrees) r e (degrees) r 8 (degrees) r 8 (degrees) r 165⁰ 180°…

A: To Sketch: the following curves: (1) y=x(x-4)(x+1)(x-2) (2) y=x2-4x+4x2+x-2 (3) y2=x3+4x2-9x-36. (4)…

Q: If f(x) = 3x² -x, then lim (x+ h) – f(x) ; h A B 6x - 1e C бх +3h — 1€ D Зх — 1€ E 6x+h– 1e

A: Derivative

Q: alculate (a) ?500 (2i + 5). i=0 (b) the sum of the first 50 multiples of 3 (starting from 3, not…

A: Given 500 (2i + 5).for i=0

Q: show that the x-intercept of the graph of Ax+By=C is (c/a,0)

A: Given equation,

Q: Find the domain of the function f(x, y) = In(3x? – 2y + 1). The set of all ordered pairs (x. y) for…

A:

Q: 9.) What is the smallest slope of the function y=x²-3x² + 5x-1 on ?

A:

Q: Find the Axis of Symmetry of f(X) = X2 - 6X + 5 %3D OX =-3 None of these. OX = 3 Y = 5

A: Given: The quadratic equation fx=x2-6x+5 To find: Axis of symmetry.

Q: Let a, ßeR ,such that 2(a -1)+ 3(a – 1)+ 6a=0 and 2(1-B)+ 3(1-B)-6B + 12=0 and a + B, also graph of…

A:

Q: 18. Use the vertical line test to determine if y is a function of x in the graph. Which of the…

A: The given problem is to check the given figure is the function of x or not using the vertical lines…

Q: Find the constants c0, c1, and x1 so that the quadrature formula Z 1 0 f(x)dx = c0f(0) + c1f(x1),…

A: Consider the given quadrature formula, ∫01fxdx=c0f0+c1fx1 here we need to determine the constants…

Q: Let f(x, y) = x²-2 y.(y+4)

A: We can compute the determinant.

Differential Equations

Have you ever observed the movement of the satellites and rockets or how the planets go around the sun in their orbits? How will you determine their motion? Definitely they follow some scientific laws and these kinds of problems are framed as differential equations.