Show that the function f(x) = x' + 3x² is continuous at every real number a.

Q: Is there a real function f(x) that is differentiable only at a point x?

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Q: f(x) = -7x + 6 x² +6 if x < 0 if x 20

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Q: x+5 4. f(x) = %3D x2-5x+4

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Q: The function f(z) is analytic if

A: analytic functions are functions which are locally given by the convergent power series. i.e any…

Q: Find the constants a and b such that the function is continuous on the entire real line x 3 a = b =

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Q: I. Is the function given by g(x)=x²-3x + 2 continuous over the interval (-4, 4)? Why or why not?

A: Function given is- g(x)=x2-3x+2 continuous over the interval (-4,4) . Wee need to determine whether…

Q: Let f(x) = x and I = [0, 1]. If P is the partition given by P = {0, 1/8.1/4, 1/3, 2/3, 3/4, 1} and…

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Q: X-2 f(x)3D x2+x-30

A: In the given question a function is given and we have to find point of discontinuity of the…

Q: Find y' if 3x2- (xy²) = 2y³ 2 3=

A: Given: 3x2-xy212=2y3   As we know that; The sum/difference rule: f±g'=f'±g' The Power law;…

Q: State why the function 2z2 - 3z + e-z is analytic everywhere.

A: See the answer below

Q: (x² + 1 if x -1

A: For function g(x) to be continuous on -1 limx→-1-g(x)=limx→-1+g(x)=g(-1)…

Q: Show that f(x) = 2a + 3b is continuous, where a and b are constants

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Q: d dx y' z' y" z"

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Q: vertical asymptote(s): horizontal asymptote(s):

A: Since multiple subparts are asked, I am answering first 3 subparts

Q: Show that the function f defined by 1. (x, y) = (1, –1) f (x, y) : x² + y .2 (x, y) + (1, –1) x + Y…

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Q: Determine the interval(s) on which f(x)=square root(x/x-4) is continuous.

A: Given query is to find the interval where function is continuous.

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

A: Given