2. Let f(x) = -x– 1. a) Find f-1(x).

Q: Show that the function f(x) = exp(−|x|) is not differentiable at x = 0.

A: We have given function fx=e-x As we know the modulus function is not differentiable at x=0.…

Q: Examine if f(x) = ln(x2+2) is uniform continuous on the interval (-∞,∞)

A:

Q: Show that the function f(x) = e¯*/2 has inflection points x = f1. at

A: We have the given function as fx=e-x22              ⋯⋯1 As we know that, a point of inflection of…

Q: Verify Rolle's theorem for f(x) = x* – 4x+8 over the interval [0, 2].

A:

Q: For what value(s) of x is the function f(x) = } 2x + 4 (x² +x +1 if – 2 sxs1 if x>1 NOT continuous?

A:

Q: the function f is not differentiable at x=0.

A:

Q: 3 Let f(x) = 2 + In(bx), where b is a positive constant. Find f'(x).

A:

Q: 6. Consider the function f Cx)=5(o+5)-25 if X#し if xfO D.IS fCx) continuous at X-0? EXPlain

A:

Q: 67. Is the function given by g(x) 1 continuous over %3D x + 5 the interval (-4, 4)? Why or why not?

A: g(x)=1x+5

Q: Q1: If the function f(x) define as f: R→ R such that f(x) = (x+1, x>2 x²-1, x≤2 Show that the…

A: This is the question to check the differentiability of the function.

Q: Suppose F 1  and F 2 are both antiderivatives of f on an interval I How are  F 1  and F 2  related?

A: Given:  F 1  and F 2 are both antiderivatives of f on an interval I. That is,

Q: 18. Suppose that f is a differentiable function such that f(g(x)) = x, and f'(x) = 1 1+(f(x))². Show…

A:

Q: What is the minimum f(x) value of f(x) = sin x on the interval [0, 2]? %3!

A: Derivative Test: find values of x for which f'(x)=0 Then find f''(x) and put values pf x from above…

Q: Suppose that f is a function on the interval [1, 3] such that –1 < f(x) < 1 for all x and f(x) dx…

A: It is given that ∫13fxdx=0 and -1≤fx≤1.

Q: What does it mean for f to be differentiable at a ?

A: we have to define that what we mean by the f is differentiable at a.

Q: Differentiate the function with respect to the independer X f(x) = +e5x + e 2 e (x) = 0

A:

Q: 6. Use an appropriate substitution to prove f(x)dr = | f(a+b- x)dx.

A: To use an appropriate substitute to prove  ∫abfxdx=∫abfa+b-xdx

Q: Prove that f(x) = x 2 takes on the value 0.5 in the interval [0, 1].

A: We have to prove that f(x)=x2 takes on the value 0.5 in the interval [0, 1].

Q: 57. Is the function given by Sx + 1, for x 4, g(x) = continuous at x = 4? Why or why not?

A: gx=12x+1,   for  x&lt;4-x+7,   for  x&gt;4 Now left hand limit at x=4 is, limx→4-fx=limx→4-12x+1…

Q: (3) If the functions f(x) and g(x) are continuous 0sxS1, then f(x)/ g(x) is continuous on the…

A:

Q: 1 Differentiate f(x) = log, x from the first principle. Note: f'(x) = x In a

A: q- differentiate the function fx=logax from the first principle it is known that, according to first…

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

A:

Q: 2) Consider the piecewise function: |x – 1| x² – 1' x 1 For what real number A is the function…

A: A function f(x) is continuous at x=a if the left-hand limit and the right-hand limit of the function…

Q: Let f(x) = x -[r] and f :[1,5) →[0,1). What is the discontinuously type of f(x) at the point x = 3?

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Q: 14. Consider the function f (x) = x²e+x . f(x) has two inflection points at x = _ and x =_.

A:

Q: Show analytically that the function f is not differentiable at x = 0. Ax) = 2x+1 x>1

A:

Q: 1. Why is f not a function from R to R if a) f(x) = 1/x? b) f(x) = VT? c) f(x) = ±/(x² + 1)?

A:

Q: 56. Is the function given by Sx + 1, for x 4, G(x) = continuous at x = 4? Why or why not?

A: As we know that  Function will be continuous at x=a if limx→a-fx=limx→a+fx=fa

Q: 6. Use the definition, determine whether the function g(x) = x = 2. Justify the conclusion. x² -…

A: The solution is given in the next step.

Q: 11. Prove from the definition that the following functions are differentiable. ()- (b) f =xy?

A: By the definition, the function f(x,y)=xy^2 is differentiable if fx(x,y) and fy(x,y) both exist.

Q: x2 – 1, if x 1 Let f(x) (a) Is y = f(x) continuous at x = 1? (b) Is y = f(x) continuous at x = 2?

A:

Q: 1. Show that function f(x)=D|x | is not differentiable at 0

A: As per company guidelines we can solve first question. I hope that the given solution will help you.…

Q: Find ao of the function f(x) 1-Cosx f(x) =

A:

Q: C. Is the function define by g(x) = x² – sin x + 5 continuous at x = n?

A:

Q: (d) A function not continuous at 0 such that (f(x))4 is continuous at 0.

A:

Q: Let 'f be a continuously differentiable real valued function defined bx+a x<1 by f(x) = 5x² Then the…

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Q: Give an example of a derivable function f (x) with f ′ (- 4) = -3

A:

Q: Show that the function f(x) = exp(-|x|) is not differentiable at x = 0.

A: Given function is  fx=e-x given point is x=0.

Q: 3-The function f defined by 2. Is f is Continuous at x=| ?

A:

Q: Show that f(x)= |x| is not differentiable at x = 0.

A:

Q: Use the linearization of f(x) 1 at x = 4 to approximate f(4.3) . - f(x) =

A:

Q: The function f(x, y) -{¹. - x² - y², 0, if if x² + y² 1 , is continuous

A: Given function is fx,y=1−x2−y2, if x2+y2≤10,             if x2+y2&gt;1. We have to check whether the…

Q: 5. Is the function given by F(x): = x = -1? Why or why not? Vx continuous at

A:

Q: Show that f(x) := x/3, x e R, is not differentiable at x 0.

A:

Q: Find the length of the curve defined as: f (x) = 5x from x = 0 to x = 1

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Q: Find the values of a and b such that f is differentiable at x = 3

A: Given,            The function is fx=ax+bx≤32x1-1x&gt;3To find : Find the values of a and b such…

Q: Prove: f(x)=5x y is continuous at x=2

A: A function fx is continuous at a point x=a, if limx→afx=fa Given function is

Q: 34. Show that f(x) = Jã is not differentiable at x = 0.

A:

Q: Is the function F(x) as given is constant, increasing, or decreasing on the interval (0, ∞)?…

A: Fx=∫x2x1t dt⇒Fx=lntx2x⇒Fx=ln2x-lnx⇒Fx=ln2xx          ∵lnx-lny=lnxy⇒Fx=ln2