Suppose that the function f: [0, 1]  in R is continuous and thatf (x)>= 2     if 0 <= x < 1.Show that f(1) >= 2.

Q: Let f(x) be a continuous function on (-00,0) and f"(x) = (-4x + 5)e4x. The function f(x) has an…

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Q: Suppose  f ( 200 , 300 ) = 1000and ∂ f ∂ x ( 200 , 300 ) = 12 and ∂ f ∂ y ( 200 , 300 ) = 10.…

A: Given, f(200,300)=1000 ∂f∂x(200,300)=12∂f∂y(200,300)=10

Q: Let 1 f(x) = 2 9, - 2 < x < 5 - The domain of ƒ¯'is the interval [A, B| where A = and B =

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Q: Determine if = f(x)=Vxis uniformly continous on the interval I [0, +)

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Q: Provide an example of a function which is continuous on all of R and differentiable on all of R…

A: The function is y=x+4 (shown in the figure above)

Q: On what domain is the function f(x) = 3 + V5x – 20 continuous?

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Q: What is an example of a function f : [-2, 2]-->R which is not differentiable at -1 but which is…

A: To find an example of a function                                   f : [-2, 2]→R which is not…

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: If f:[-5, 5 ] to R is a differentiable function and if f'(x) does not vanish anywhere, then prove…

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Q: Suppose f is continuous on [1,5] and the only solutions ofthe equation  f(x)  = 6 are x = 1and x= 4…

A: Given: The function f is continuous on 1,5 and fx=6 has only two solution x=1, x=4 and f2=8, To…

Q: Letf(x) = x³ - / x² + + 28x. Locate any critical points for f. Then use the First Derivative Test to…

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Q: Let f be a function defined on [15, 23]. Suppose for every x ≤ (15, 23) d da If f(16) = 44, find the…

A: We  know By definition of derivative  in interval a,b⇒f'x=limx→afx-fax-a

Q: Suppose that f is a continuous function such that | f(x) dz = -12. Find | () dr.

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Q: If the function is defined y=2x when x=3, is this function differentiable at x=3? Also, is this…

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Q: Let f be a function that is continuous on [1,7] and differentiable on (1,7). Suppose 2 < f'(x) < 3…

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Q: Find f(2021) if function f satisfies following conditions: f(1)=1, f(x+y)=f(x)+f(y), for all x,y…

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Q: Suppose that f is continuous at (4, 6) and that f(4, y) = y' for y + 6. What is the value f(4, 6)?…

A: Given that f is continuous at 4,6 and that f4,y=y3 for y≠6. We have to find the value f4,6. Since,…

Q: Suppose we have a function f on an interval [a,b] where f(a)=f(b)=0 and f''(x) <= 0 for all x on the…

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Q: Construct a continuous function that shows that the intervals [0,1] and [2,6] are homeomorphic

A: In the given question we have to find a continuous function from the interval [0,1] to the interval…

Q: Use the intermediate value theorem to prove that any continuous function with domain [0, 1] and…

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Q: Is the function 1 >-{ f(x) = √x x3 x < 0 0 ≤ x ≤ 1 piecewise continuous or piecewise smooth on [-1,…

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Q: Let the function f:R-->R be twice differentiable and suppose that f(x)≤0 and f''(x)≥0 for all x.…

A: It is given that, the function f:R--&gt;R be twice differentiable and suppose that f(x)≤0 and…

Q: Suppose that f(x) is a continuous function on the interval [0, 4] with f(0) = -10 and f(4) = 10.…

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Q: Sketch a possible graph of the function f given the graph of f' below. Assume that 3. f is…

A: A discontinuous graph of f' is given Both pieces of the function of the form of parabola. Assume…

Q: Draw the level curves for the function f(x,y) = x2-y. Show five level curves within the limits…

A: We shall use MATLAB to solve the above problem.We are using computer code so that it will be very…

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.