Which of the following functions f: R → R is continuous at the point 0 € R? f(x) = x² f(x) = = X {² f(x) = { √x 0 f(x) = = x x + 2 -1 f(x) = = {i² 1 if x ≤ 0 if x > 0 if x ≥ 0 if x < 0 if x ≤ 0 if x > 0 if x < 0 if x > 0 Choose... Choose... Choose... Choose... Choose... <> O <>

Q: Determino whefuer Continuous are O fra) = x-4 x-2

A: Since the denominator is zero at x = 2. So the function is not defined at x = 2.

Q: he absolute extrema of J(*) = ,2+2x +9 n(-1,5]. %3D

A: The given function is  f(x)=xx2+2x+9 on [-1,5]

Q: Please

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Q: Q3-A) Is the function F(Z) continuous or not at z-U? 1+|21,

A: Let z = x+iy then Re(z) = x and |z| = √(x^2 + y^2) If z = 0 =&gt; x = 0 and y = 0

Q: If  f′(x) < 0 for 1 <x< 6, then f is decrescent over(1,6) True or false and why

A: If  f′(x) &lt; 0 for 1 &lt;x&lt; 6, then f is decrescent over (1,6) True or false and why

Q: Let f be a differentiable function such that 2 < f'(x) < 4 for all values of x. Show that 10 < f(12)…

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Q: 3. Find the domain of the following functions: a.) f(x) = V1-x Inx b.) f(x) = Vx - 1lr

A: solutionsince the given (3)(c)f(x)=1-xlnx(b) f(x)=x-l ln(x)use have to find the domain of the…

Q: Find constants a and b such that the function 3– bx, if x>-2 f(x)=- -1, if x=-2 ax – bx, if x<-2 |…

A: Given query is to find the value of a and b.

Q: IfY C X, show that inf (X) < inf (Y)

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Q: Consider the functions f(x)= [x²-9 x*-1 2x ; x=-1 and (3x+2 g(x) = { x=-1 Define the new function…

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Q: (3-x, xs1 Consider the function given by f (x) = Is the function continuous, %3D x -x+1, x>1…

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Q: Give an example of an everywhere-continuous function h(r) that is differentiable at every real…

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Q: Show that the function f(x)=x|x| is continuous and differentiable at x = 0

A: To show that f(x)=xx is continuous at x=0 To show that limx→0xx=00=0 use piecewise definition for…

Q: Determine whether f is continuous at a = -1.

A: Given- fx=x2-1x+1   if x≠-16           if  x=1 To find- whether f is continuous at x=-1 or not.…

Q: Which of the following functions is differentiable for all values of x? a. fAx) = 2r' + 5x² b.…

A: Given problem:-

Q: Let f(x) = x. Show directly that f ∊ R[0, 2]

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Q: Show that the given function is not analytic at any point but is differentiable along the indicated…

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Q: 17. Sketch the graph of f(x) = { 2x + 2, x ≤ −1 [x³−x, x>−1 and find the derivative. Determine…

A: 17. Sketch the graph of  and find the derivative.Determine whether  satisfies the conditions of the…

Q: The interval in which the function is decreasing is at x2 бх + 1 2 x3 y = 3

A:

Q: Let f be a real-valued function on R. Suppose that f(−1) = 3 and f'(x) ≤ 2 for all values of x. How…

A: f(-1)=3f'(x)≤2Integrating w.r.t x;∫ f'(x) dx ≤ ∫2 dxf(x)≤2x+Cf(-1)=33=2(-1)+CC=3+2C=5