c) Let S= {-1, 0, 2, 4, 7}. Find f (S) if i. f(x)=[x/5]. ii. f (x) =L (x² + 1)/3 %3D %3D

Q: 13. If f(x) = 1 / (5 + 7x) , find S f(x) by using a u-substitution. Show the u-substitutions.

A: Given, fx = 15 +7x  We have to find ∫fx using u substitution

Q: Suppose that T(0) = a and T(1) = b are some constants. Define the running pairwise average as, for n…

A: Given: Tn+2=12Tn+1+Tn for n≥0 T0=a T1=b To find: The limit of Tn as n→∞.

Q: What are the global max and min over the interval x E [0, 0) for the graph of f(x) f(x) = (X e)-3x

A:

Q: (5) Consider the several variable function f(x, y, z) = xe²y + yeš + ze¬². Give a general formula…

A: The given function,   fx,y,z=xe2y+ye3z+ze-x

Q: The critical point of the function f(x, y) = x² – 4xy+ 2y² + 4x + 8y – 1 is: Select one: О а. (4, 6)…

A:

Q: 9. If f(5) = 10, f ' is continuous, and f '(x) dx = 15 18, what is the value of f(6)? %3D f(6) =

A:

Q: Given the function h (x) = : x+1 Over what interval(s) is h (x) decreasing?

A:

Q: ,15 15 ** Let f be a continuous function. If f(x)dx = 15 and f(x)dx = -8, then f(x)dx equals -5 В C…

A:

Q: Find the linearization L(x) of the function at a. f(x) = cos(x), a = 77/2 L(x) =

A:

Q: of of and Find for the following function. f(x.y) = e xy In (2y) of dy

A:

Q: 1,3 2,1 3,4 f(x) 2,6 3,5 3,2

A: The given tabular data is,

Q: 18: Which of the following functions has no critical points? A: f(x) = -x² + x² B: C: f(x) = x³ + x2…

A: This is the question of multi-variable calculus.

Q: 2. Suppose that X is normally distributed with u =-7 and o2 P(X 2x) = 0.84. 14. Find the value of x…

A:

Q: Find the value(s) of k that makes the function continuous over the given interval. 0 sx s2 2 < x s…

A:

Q: If f(x) is an even, continuous function for which = 4 and dx = 4, then f (x) dx 3 2

A:

Q: 2 If f is continuous and f(x) dx = 14, find | xf(x?) dx.

A:

Q: 10 a- Let X1, X2, ..,Xn~N(0,0) and T Find %3D X2 E (T),Var (T)

A:

Q: Find the Wronskian for the set of functions {e¬*, xe¯×, (x + 1)e-*}.

A:

Q: 2) An elastic tire is described by the iven by the function f(x, y) = 4xy. Use

A: Introduction: The Lagrange methodology is employed to maximize or minimize a general performance…

Q: (b) Determine e so that п п c£[(x; - X;)² i=l j=1 is an unbiased estimator of o². s2 ogunl to

A: 6. From the given information, X1,.....,Xn~f be an iid random sample with mean μ and variance σ2. a)…

Q: let x has the p.d.f (11e-11x 0 < x< ∞ 0. W f(x) = Find m.g.f and prove that E(x) = M,(0)? %3D

A: We want to find the Mx(t) and E(x)

Q: 1. Find the discontinuity point/s of f(x) =

A: Since you have asked multiple questions in a single request we would be answering only the first…

Q: Maximize f(x, y) = 3xy Зху subject to x + y = 1

A:

Q: d 2 Compute f(g(x)), where f(x) = - and g(x) = 5- x. %3D dx X

A:

Q: Find the value(s) of k that makes the function continuous over the given interval. a < k k < a S 3x…

A:

Q: e +1 Differentiate the function f(x)= In 5x +1 Se+1 3ex+1 Sesz e3x +1 ,5x +1 e 3e3z Sesz e3x +1 5x…

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: suppose that y is an implicit function f(x) defined by the equation x^3 + y^3 = 8xy − 7. find the…

A: suppose that y is an implicit function f(x) defined by the equationx3+y3=8xy−7. find the equation of…

Q: 1. Find grad f for the given function below. Ax, y, z) = 5xy + 3yz – 4zx

A:

Q: Suppose that T(0) = a and T(1) = b are some constants. Define the running pairwise average as, for n…

A: Given: Tn+2=12Tn+1+Tn for n≥0 T0=a T1=b To find: The limit of Tn as n→∞.

Q: 1 Let H(s) Using convolution to find h(t) s2 (s-a)

A: Inverse Laplace transferom

Q: 8 Ay 10- | f(x) dx using Compute the following estimate of 8- y = f(x} the graph in the figure. 6-…

A: Given: The graph of the function f(x) The integral ∫08f(x)dx.

Q: If (a,ß) is a saddle point of the function f(x,y)=20y²-y³+3x2-6xy, then a+ß=

A:

Q: Suppose there is no known formula for g(x), but we know that g(2) = -1 and d (z) = V2 +5 for all x.…

A:

Q: If f(x) = x(e*+) , then f'(x) = %3D (A) (e + x³) x(e²+x²-1) (B) (e" + 5x*) In(x) æ(c*+z*) (C) (e* +…

A: To find f'(x) for the given function

Q: Please see picture

A: Introduction:Here, MX (t) denotes the moment generating function (mgf) of the random variable X;…

Q: If b > 3 and average value of f(x) = 6x – x² on the interval [0,b] is 6, then what is b equal to?

A:

Q: 4.18 Given that g(x) > 0 has the property that 6. show that is a pdf. f(x, y) 2g g(x) dx = 1, (√x² +…

A:

Q: 9 3 Iff is continuous and f(x) dx 8, find f(x2)dx

A: Given as

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: 2. Evaluate f(x) = e3x + 2 at x = -1. Round to the nearest thousandth. %3D %3D f(-1) = ...

A:

Q: (1) Find ôf/ôx, and f/@yôx of the following functions (a) f(x,y) = x²y + x²y2 (b) f(x,y) = 10x + In…

A: To find ∂f∂x and ∂2f∂y∂x of the following functions. fx,y=x2y+x2y2 fx,y=10x+lnxy fx,y=x3+5xy−y2

Q: (2) Is the function f(x) : R → R, sin a 1 ifa # πh,k & Z, ifa = Tk, k ε Z f (x) Borel measurable?

A: Consider the given function, fx=1sinxifx≠πk,k∈Z1ifx=πk,k∈Z   Thus, the given function have infinite…

Q: If (a,B) is a saddle point of the function f(x,y)=27y2-y3+3x²-6xy, then a+ß=

A:

Q: a) Find the marginal pdf's of X1 and X2 b) Are X1 and X2 independent? Why or why not? c) Find P(X1 <…

A:

Q: If (a,B) is a saddle point of the function f(x,y)=21y2-y3+3x2-6xy, then a+ß=

A:

Q: If f is a quadratic function such that f(0) = 9 and f(x) x2(x + 1)3 dx is a ratianal.functian,,find…

A: This question is about finding f'(x)  at x=0  where f(x) is a rational function

Q: 1. Use the Gauss forward formula with xo = 2.0,h = 0.15, n = 7 to find an estimate for f(2.5) if %3D…

A: Given: fx=xlnx. x0=2.0, h=0.15, n=7.   We can solve this by using Gauss forward formula

Vertices Of An Ellipse

In the study of the conic section of the geometry, An ellipse is a plane curve surrounding two focal points, or foci where the set of all locus of points in the plane has their sum of the distances to the two foci is constant. On the ellipse curve, it is the intersection point of the main axis. In an ellipse graph, the center of the axis is the midpoint of the line segment connecting the foci. The major axis is the line section that runs through the ellipse's foci, while the minor axis runs through the middle and is perpendicular to the major axis.. The ellipse has two endpoints on the major axis which are known as the vertices (in plural), vertex in the singular. The equation of the major axis is 2a, the equation of the minor is 2b and the distance between the major axis and minor axis is 2c. The semi-major axis has a length of a and the semi-minor axis has a length of b. The ellipse's vertices are determined by the elliptical orbit's equation and graph.