Continuous on [0, 3], ƒ(1) = –1, f(2) = 1 and not differentiable at x = f(r)

Q: What are all absolute and relative extreme values of the function f(x)=– sin z on the interval (0,…

A: Given function f(x) - f(x) = -sinxDifferentiating on both sides with respect to x - f'(x) =…

Q: Suppose that f(x, y) is continuous at (2, 3) and that f(2, y) = y3 for y ≠ 3. What is the value f(2,…

A: Given that f(x, y) is continuous at (2, 3) and that f(2, y) = y3 for y ≠ 3. We have to find the…

Q: Is there a smooth (continuously differentiable) curve y = ƒ(x) whose length over the interval 0<=…

A: Given there is a smooth (continuously differentiable) curve y = ƒ(x) whose length over the interval…

Q: Show that the function y=| × | is differentiable on (-o,0) and (O, c0) but has no derivative at x =…

A:

Q: The function f(x) is differentiable on (0, 1) and satisfies f(0) = f(1). However, its derivative is…

A: Consider the given function: Here the objective to check whether the given function contradicting…

Q: What conditions must be satisfied by a function if it is to be continuous at an interior point of…

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Q: tion f defined as xy Ax, y)=- when (x, y)#(0, 0) when (x, y)=(0, 0) =0, is continuous at the origin.

A:

Q: . Show that the following function is differentiable everywhere on R but of which the derivative is…

A:

Q: 3. Is the function given by x²-4x-5 -,x< 5 f(x) =. x-5 x+1, x 2 5 continuous atx=5? Why or why not?

A:

Q: If the derivative of y=f(x) does not exist at X = a then y f(x) is not continuous at X = A) True B)…

A:

Q: The limit cos(x) +1 lim x – 9T represents the derivative of some function f(x) at some number a.…

A: In the given question, f(x) is cos(x) and a is 9π

Q: All edges of a cube are expanding at a rate of 6 centimeters per second. How fast is the surface…

A: We have to solve above problem.

Q: Why is the function f(x)= cotx not differentiable on the interval [0, pi] ?

A:

Q: Assume that f : (0, 1) → R is a differentiable function with the derivative f' increasing on (0,…

A: Given f:0,1→R is a differentiable function and derivative of f is increasing in 0,1 that is f'x&gt;0…

Q: Jaimie, a MAT student, claims that "For a continuous function f(x), defined on an interval [a, b],…

A:

Q: What value for a will make sinx { ,X # 0 2x f(x) = %3D 3D ,X = 0 a continuous function?

A: For a function f(x) to be continuous at x = a,limx→a-f(x) = limx→a+f(x) = f(a)

Q: Let f(x) be a function that is defined and has a continuous derivative on the interval (2, 0).…

A:

Q: ion ƒ(x) is infinitely differentiable and that f'(x) = - st, second, third and n-th derivative of f…

A:

Q: What is the Extreme Value Theorem for continuous functions?

A: Extreme Value Theorem According to this theorem, if a function y=fx is continuous in a given…

Q: x² – 16 f (x) = x( x 2(х — 1)°(х — 2) : о 1)8 (x – 2) : 0 - -

A: If the given function is equal at LHL and RHL at x=3 then the given function is continuous at x

Q: Let f(x) = Cx + 7x if x< 4 x³ - cx if x2 4. For what value of the constant c is the function f…

A:

Q: Where is the function defined by f(x) = In (x) increasing? Where is f(x) decreasing? Where is the…

A: Given a function: f(x)= ln(x) and the function is defined in the domain x∈(0, ∞)Then, f'(x)=1x

Q: The graph of f', the derivative of the function f, is shown below for the interval 0<xs10. The areas…

A:

Q: True or False The graph of y = cos x is decreasing on the interval (0, π).

A: True or False The graph of y = cos x is decreasing on the interval (0, π).

Q: If f(x) is odd function, then the derivative of y=sinh (f (-x)) equals Select one: o y'=Xf'x) – f x)…

A: Differentiate wrt x

Q: Find local extrema using the second derivative test for the following function: f(x) = x In x

A:

Q: Let y = 5−2x be the tangent line to a function y = f(x) at x = 3 and y = 2+3x is the tangent line to…

A:

Q: Is it true that every function y = ƒ(x) that is differentiable on [a, b] is itself the derivative of…

A: Any function y = ƒ(x) is said to be differentiable on closed interval [a, b], it should be…

Q: The slope of the tangent line to the differentiable function f at the point (2, f(2)) is…

A: It is given that the slope of the tangent line to the differentiable function f at the point 2,f2 is…

Q: Find the x-value of the extrema by using the Second Derivative Test. Justify your answer. f(x) =…

A: As per the question, we need to find out the x value of the extreme, for bubble 3 only. For (3),…

Q: How can you sometimes decide from examining ƒx and ƒy that a function ƒ(x, y) is differentiable?…

A:

Q: True or false? The function f(, y) is continuous at x² + y? the origin. O True False

A: We have to check three condition for continuity

Q: Show that the function f(z) = sin x cosh y + i cos x sinh y is continuous as well as analytic every…

A:

Q: are differentiable at a, then prove the sum and product rules for derivatives. If f, 9

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Q: Suppose that f: R² R is a function given by y³ x² + y² f(x, y) = 0 for x = y = 0. Show that f(x, y)…

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Q: question. sf continuous at x = - 3? AY 5- 4- 3- 20 -5 -4 3 -2 -14 123 4 5 -2- -3- -4- -5-

A:

Q: The Bisection method is based on the principle that a continuous function which is positive at one…

A: Consider the provided question, We have find the value after third bisection process of the function…

Q: Find the values of a and b that make f continuous everywhere. x2 – 4 - 4 if x < 2 X - 2 f(x) = ax2 -…

A: Here, we need to find the values of a and b. We are given that f is continuous everywhere.  So,…

Q: 4. "The function f(x)= x-1 is continuous on(-o, 00)". Is the statement true or false? If it is…

A: Hi there, i have explain that if x tends to 1 from right side the function will give +1 and while…

Q: Find the particular antiderivative of the derivative f'(x) = 3 -+x that satisfies the condition f…

A: Follow the procedure given below.

Q: True False Suppose f(x) is differentiable at x=a. Then f also continuous at x=a.

A:

Q: consider a continuous function y=f(x) whose first derivative is y'=x(x- 2).

A: We can find the interval as below.

Q: Let f(x) be a function that is defined and has a continuous derivative on the interval (2, 0).…

A:

Q: Would it be possible for a function to be continuous on [0,2) but not on [0,2]?

A: Let us consider the function f(x) =(x+4)/(x-2) .

Q: Suppose we know that f(x) is continuous and differentiable on the interval (-7,0], that f(-7)=-3 and…

A: fx is continuous and differentiable function on the interval -7, 0, f-7=-3 &amp; f'x≤2.

Q: What does it mean for a function to have an absolute extremevalue at a point c of an interval [a,…

A: When an output value of a function is a maximum or a minimum over the entire domain of the function,…

Q: True or false: if f is continuous at a, then the derivative of f exists at a. If it is false, can…

A: To find  -- if f is continuous at a, then the derivative of f exists at a or not.

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.