Suppose that the functions u and w are defined as follows. =u(x)=x^2+6 w(x)=√x+1 Find the following. (u∘w)3= (w∘u)3=

Q: Give Three Functions  of Wronskian ?

A: To Give: Wronskian of three functions.   Wronskian:

Q: (-х+а, х < —1 If f(x) = {x² + 5, –1 < x < 2 is continuous then х — b, х 2 2 a + b =?

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Q: im (x²-C² if X<4 1 f(x) = {(x+5 x²-c² (x + 5 if x = 4 lim

A: Given:-x2-c2   if x&lt;4cx+5    if  x≥4f(x) is continuous at x=4solution:-if f(x) is continuous at…

Q: Find max and min of function on the interval    f(x)=-x4-x3+5x2-4 on [-2,1]

A: The given function is; f(x)=-x4-x3+5x2-4 on [-2,1]

Q: り If X~メ (2)、 Find the 32-moment of x about zero

A: Introduction: The random variable X has a chi-squared distribution with 2 degrees of freedom, that…

Q: 4 Determine if f (x) = - 2x if x 1 is differentiable at a = 1.

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Q: Show that the functi on When x g 0 f(x)= +1 0 . When x = 0 is discontinuous at x = 0.

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Q: (4-х, XS0 10) Determine if the function y(X) = 3x, is differentiable at x =0. x>0

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Q: 6 Use the Linear Approximation to estimate Af for f(x) = when a = 2 and Ax = 3+x2 (Use decimal…

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Q: Show that f(z) = 3z2 + 2z + 5 is analytic function.

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Q: Suppose that y is a function of x. Find if 2x°y 3 2y + 5. - -

A: We will find out the required value.

Q: Find a polvnomial f(x) of degree 4 with real coefficients and the following zeros. 3,-4, 2+i 1) - 0…

A: Given,  The zeroes of the 4 degree Polynomial f(x) is 3, -4 , 2+i and 2-i.

Q: If - 2x +1 ,when X#! and fcx)= 3 when x= 1 show that The function fex) Continuous at X - 1

A: The detailed solution is as follows below:

Q: Suppose that z = f(x, y) is implicitly defined as a function of x and y. Determine for 4x²z³ - 5yz²…

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Q: To plot the function f(x) == %3D 2x over [0,5], we use fplot('exp^(-x) /2*x'[0,5)…

A: Since we are given with multiple number of questions and our guideline is solve the first question…

Q: (3) Show that the function is discontinuous on the specified interval. Vx2 - 64 if x < -8 if -8 <x <…

A: Note: According our answering guidelines we have to answer only one question (if there are multiple…

Q: Find and classify the stationary points of f(x) 2x} + 4x,x3 – 10x,x, + x}

A: Given,     f(x)=2x13+4x1x22-10x1x2+x22

Q: Show that the function f(x) = K. when xw0 when xois discontinuous at x = 0.

A: Solution

Q: Find the derivative of f(x) = 2² +8-2³ + 5z³. 0 (2) - 1/2 +8-235-24 + 152² O f(2)=1/22-²5 2¹ +152²…

A: The given function is; f(x)=x2/4 +8 - 5x5/3 +5x3.

Q: X = (1-_-_-_-)* 2 o then f(x) tend:

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Q: Find the interpolating polynomial for the function f(x) = e through the points x = 0, 1, 2.…

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Q: for x 2 - X Is differentiable at x = 2 but not at x = 1.

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Q: B)Is w = Zez analytical function or not?

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Q: what is the quadratic polynomial for the function f(x,y) sin(xy) + cos(x/y) at (pie/4, 1) (show…

A: We will find out the required value.

Q: Determine where the function F(x)=8x/x2+4 is continuous. The function is continuous on ?

A: Suppose   are continuous function at then rational function is continuous at   if .

Q: Suppose f is a f(8(x))=2x² and differentiable function where 2x f'(x)=2+ f (x). Show that g'(x)=…

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Q: Find a function flx) such that f(x) -llex and %3D 3. f(0)-- 주

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Q: when that this 1x² + y² Shothathis sho (x, y) (0,0) and f(0,0) function is continous at (0,0)

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Q: 5. * y = ( In æ)²

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Q: 4.x +1 1 with f'(x) = 1/ 56x2 - 156x + 115 14x – 19 - - 3. Let f(r) = and f"(x) 4 %3D 3 5 Vr2 – 3x +…

A: To find the points on which it is concave up or concave down

Q: Suppose that f(x,y,z)=x^2yz−xyz^3 is a function of three variables.

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Q: Find the critical numbers of the function. f(x) = x³ + 3x² – 24x

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Q: Suppose that f(x, y) = yVx³ + 1 on the domain D = {(x, y) | 0 < y <x < 3]

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Q: GRuen that the divectional deivative of f(x,4,2) out the point (3,-2,1) in the divection of a=…

A: Given a→=2i^−j^−2k^ and directional derivative of fx,y,z at the point 3,-2,1 in the direction…

Q: Consider the relation x2z2 = arctan (xyz) + 4, which defines z as an implicit function of x and y,…

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Q: Q1) check the continuity of fX) at X--1, 0,1.2,3 -1<x<1 f(x) = 2x-1, 3x-2 2SxS3 2, 1=3

A: As per the answering guidelines we need to answer only first question so please repost the other…

Q: 13,4) f(x.y) =In(x + x² +y² If Find x

A: f(x,y) = ln (x+x2+y2)∂f∂x=∂ ln (x+x2+y2)∂x=1 (x+x2+y2)×(1+12x2+y2)×2x

Q: For what value of the constant c is the function f continuous on (-∞, 00) ? if x < 3 cx2 + 8x F(x) =…

A: To find: The value of c if function is continuous at -∞,∞. Given: The function is fx=cx2+8x   if…

Q: [1, 2). over Calculate M6 for f(x) = 3 · In(x³) M6

A:

Q: Use Intermediate Value Theorem to explain why the function has a zero in the given interval. [0. 1]…

A: Given problem:- Use Intermediate Value Theorem to explain why the function has a zero in the given…

Q: 8(x) = X -x3 + 2x x4

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Q: Identify the removable discontinuity. f(x) =  x3 + 2x2  over  x + 2

A: Given query is to find identify the removable discontinuity.

Q: What are the critical numbers of the function f(x)= 2x^(3)-2x^(2)-16x+1?

A: Let's find.

Q: Show that f(z) = 3z² + 2z+5 is analytic function.

A: Given

Q: Find domain and range of the funetion f(x, y) In[e-x' -y'1

A: The ln function is undefined for negative arguments. This will ensure that argument is positive. So…

Q: inh´x + cosh²x = 1 = x²arccsch(x²) then f

A: 1. The function fx=y=coshx is represented as , coshx=ex+e-x2 To check whether the function is odd…

Q: defines 2 as y. y- cos (3x2) = 5 a function of x and • differentiate implicity to find az ду

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Q: If f(z) is analytic with constant modulus show that f(z) is constant u=3x²y+2x²-y³-2y²

A: To Proof :-  If f  z is analytic with constant modulus , show that f  z is constant.  Given :-  The…

Q: Show that the following function is a concave function on R: f(x,,x,)=-x} - x,x, – 2x² Then, Find…

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Limits

When it comes to calculus, limits are considered to be a very important topic of discussion. The main importance of limit lies in expressing the value of a function as it gets closer to a certain value. Also, limits can help you to understand other topics, such as continuity and differentiability better. In a broader sense, every calculus notion is a limit. Other branches of calculus have also been derived from limits.