Q5: State and prove the theorem of (continuity-differentiability), then find the value(s) of x that makes y continuous but not differentiable by writing the required procedures to that If: X, (1) y = {2x x20 x < 0 (2) y = {(x - 2)², 1>x, x>4 X 1≤x≤4 Gunations) then use it to answer

Q: Prove algebraic ally that any function of the form f(x)=ax2n+4 (where n is an integer) is symmetric…

A: The given function is fx=ax2x+4. To prove fx=ax2x+4 is symmetric to the y-axis, it is enough to…

Q: 2x - 3x + 13x+a if x#2 f(x) = . X-2 b if x = 2

A: Solution:- It is give that f(x) is continuous at x=2  and the given function is  f(x)=…

Q: Let f:R-->R and suppose that |f(x)-f(y)| less than or equal to |x-y|^a for some a>1. Show that f…

A: Let f:R--&gt;R and suppose that |f(x)-f(y)| less than or equal to |x-y|^a for some a&gt;1. Show that…

Q: Show that f[x0, x1, x2] = f[x2, x1, xo].

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Q: ) Is the function f(x) = differentiable on the open interval (-1,1)? x².

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Q: 5. Let f(x) = x-3x73. Use calculus to determine the critical numbers for the function.

A: Consider the  provided function, fx=x-3x23 Find the critical point of the critical point. Find the…

Q: (lx) +3, x≤-3 Q4) Check the continuity of f(x) = -2x -3<x<3 " (6x + 2, x ≥ 3

A: To check the continuity of given function,

Q: Let f be the function given by f(x) = Jax + b for x 2 where a and b are constants

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Q: Find x-intercepts of the function: x2 – 9 f (x) = Зх + 1 Select one: O a.x = 3 O b.x= -3, x= 3 C. X=…

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Q: Let f(x) = 1+ V7x +1. Determine the largest possible domain of f(x) Select one: • [-1/7, +o0)

A: Given function is  fx=1+7x+1

Q: Consider the function f(x) = 12x5 + 45x4 - 80x³ + 3. f(x) has inflection points at (reading from…

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Q: True f must be continuous in its domain? or false: If f(x) is differentiable in its domain then

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Q: If f (x) = x² - x and g(x)=√x-2, what is (fog)(x) ? Simplify your answer. x²-x-2 /x² - 2 2-x-2 O…

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Q: Q3) Test the continuity of the function f(x): -15x <0 0S X< 2 F(x) = 2х— 1 x+ 3 X = 2

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Q: What are intervals of concavity of the function f(x) = -2x + 6x² – 3 ? a. Concave upward on (-1, o0)…

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Q: (x2+3). Explain why √x4+24 Q7. Consider the function f : [0, 1] → R, x→ (a) f continuous, (b) f is…

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Q: Choose the correcty symbol which represent relation between I2 and I1 correctly.

A: Function is the unique relation where each x is mapped to unique y. It can be of many type,…

Q: 58. Show that if f is a function and z = x+h, then f(2) – f(x) _ f(x+ h) – f(x) Z - x h

A: This question is taken from the function in which we have to prove the given equation. We can write…

Q: Let f(x) = 8x3 - x4 + 4. 1. Find the interval of concavity.

A: Find the second derivative of f(x) and equate it to zero f(x)=8x3-x4+4 f'(x)=24x2-4x3…

Q: Let a and b be real numbers. Consider the function y = f(x) = 1x² ax+b For which values of a and b,…

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Q: + 3x - 6x if xs-2 if x>-2 A) Check the continuity of the function f(x) at x =-2 f(x) =

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Q: f (x) = x 2 satisfies the Horizontal Line Test on the domain {x : x &gt; O}.

A: Horizontal line test is a test used to find the function is injective that is one-to-one. First…

Q: Since f(x) is continuous between a and b, the function needs to cross the x-axis. O TRUE O FALSE O…

A: Given fx is continuous between a and b