let f: R-->R be given by f(x)= 3x^2 a. Show that f is NOT one-to-one b. is f onto? Explain

Q: Show that f1x2 Vin x is right-continuous at x = 1.

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Q: Explain the Wronskian of 2 functions f and g ?

A: Let f and g are the two functions. The Wronskian of the n functions is the determinant of the matrix…

Q: For what codomain is f(x) an onto function? а. y4

A: Given: To identify that for what co-domain is function f(x) is onto function. Definition: Onto…

Q: Ex/l let fi [1₂1]-> R be function f(x) = 3 x70 2 x < 0 Is the function integrable and Continuous?

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Q: 8. Is the set of functions f₁(x) = 3e³x and f₂(x) = -3e3³* independent? Show using the -3.x…

A: Given functions- f1x=3e3x  and  f2x=-3e-3x To show whether the given set of functions is independent…

Q: The function f, where f(x) = secx, has domain 0<x< and has inver %3D f-l, where f-(x) = sec-lx. Show…

A: The given function is f(x)=sec x and the inverse function is f-1(x)=sec-1x. To prove that…

Q: Suppose that ƒ'' is continuous on [a, b] and that ƒ has three zeros in the interval. Show that ƒ''…

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Q: Aside from Extreme Value Theorem (EVT), there is another theorem behind optimization, the Fermat’s…

A: Given that f is a continuous function on an open interval I where c is in I. Since, I an open…

Q: Determine whether f is continuous on its domain. If it is not continuous on its domain, say v…

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Q: Define a weakly quasi-concave on a Cobb-Douglas Function

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Q: Show that the functions are continuous on their natural domains with examples?

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Q: 4. Is the function f integrable over the interval [-4,1]? Briefly justify your answer. 2x2 + 5x – 3…

A: Solution  Question 4  Given,  fx = 2x2+5x-3x+3  We have to find the function is integrable in the…

Q: Theorem

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Q: IF Function F is bounded on [a,6], does F has as abs ,max and abs. min not ? or

A: We have a example such that that is bounded but not attains either absolute maximum or minimum.

Q: If f is integrable on the interval

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Q: Let F (x) = %3D In tdt then F' (x) = et3

A: To find F'(t)

Q: Is a function Continuous ?why? integrable anod

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Q: If f (s Continuous then on -fex) True or felse?

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Q: Let x be a continuous Click the icon to

A: Given that X be a continuous random variable with a standard normal distribution.  We have to find…

Q: Show that f is continuous on (∞ , -∞ )  .

A: we have to show that f(X) is continuous in (-∞,∞). f(x)=x2             if   x&lt;1           x…

Q: Every bounded continuous function is integrable.

A: We have to indentity the given statement as true or false.

Q: (2) Are all entire functions differentiable on D?

A: Here we check whether given statement is true or false. Are all entire functions differentiable in…

Q: Define wronskian of Two Functions?

A: Wronskian of two function: Let f(x) and g(x) be two differentiable functions, then wronskian of f(x)…

Q: Use f- calculate to (f!) in the damain of f= ==-1, %3D

A: Given: f-1(x)=1x-1 ;          14≤x≤1

Q: Give an example of a function that is not Riemann integrable.

A: To give example of a function that is not Riemann integrable :-

Q: Show that the function is continuous on its domain. State the domain. Vx + x cosx

A: fx=x4+x3 cosx The domain is the set of all positive real numbers including zero. That is, the domain…

Q: Find the number of all onto functions from the set {1, 2, 3, ... , n} to itself.

A: Consider the given set {1, 2, 3,…, n}Since the function is onto. So, all elements of {1, 2, 3,…, n}…

Q: Assume that fis differentiable on asxsb, a b, and that f(b) <f(a). Show that f is negative at some…

A: Since you have asked multiple question, we will solve the first question for you.If you want any…

Q: Let f:C-R be a function where Cis a closed and bounded interval. Prove that if f is continuous then…

A: The given problem is to prove that the function is maps from closed and bounded interval to Real…

Q: Integrate to find F as a function of x, and demonstrate the Second Fundamental Theorem of Calculus…

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Q: Use the Second Fundamental Theorem of Calculus to find F '(x) F(x) |Vt4 + 1 dt -7

A: 2nd Fundamental Theorem : For F(x)=∫axf(t) dt, if f is continues on [a, x], then F'(x)=f(x).

Q: Every continuous function on a, b, that has absolute extrema on endpoints, must have one critical…

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Q: 7. Where is f(x.y)= continuous? Do not just write an answer, show your work or give any necessary…

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Q: find the value of c that make the function continuous

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Q: Use part I of the Fundamental Theorem of Calculus to find the derivativ f(x) Vt3 + 2°dt f'(x) =…

A: Given query is to find the derivative.

Q: Which . functions are continuous through its domain?

A: Continuous Function: A function fx is continuous at a point c of its domain if  limx→cfx=fc A…

Q: Suppose f is a bounded real function on [a, b), and f' eR on [a, b). Does it follow that fe R? Does…

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Q: Determine the set of points at which the function is continuous

A: f (x, y, z) = sin-1 (x2 + y2 + z2) = t (Let's say)Hence, sin t = (x2 + y2 + z2)

Q: Show that if f: I¬R where I is open interval in R, is differentiable at point p in R then 'f is…

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Q: example of a function fi[g1] IR Give which is not integrable

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Q: Verify the Mean Value Theorem for f(x) = In(6x + 1) on | 0, %3D

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Q: estimate the type of the function at the interval {(1,2), (2,5), (3,5), (4,7)} is it: 1-1 or onto..?

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Q: Is g continuous on (3, 5)? Is g continuous on (6,+∞)?

A: We know that a function gx is continuous at a point p if,limx→pgx=gp.We need to check the continuity…

Q: Give an example of a function that is integrable on the interval [−1, 1] but not continuous on [−1,…

A: Let fx=x       Greatest integer function. Now, ∫-11x dx=∫-10x dx+∫01x dx=∫-10-1 dx+∫010…

Q: Determine if continuous f (x) = V4-x at x=0 %3D

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Q: Define a function f(x) by the rule if x is rational and f (x) = if x is not rational. Prove that f…

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Q: Determine whether f is continuous on its domain. If it is not continuous on its domain, say why. 1…

A: Need to find continuous and discontinuous of function

Q: (4) Are all entire functions bounded on D?

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Q: 3. Show that 5 x + 7 is a continuous fimction

A: Let, f(x) = 5x+7 be defined over R, the set of all real numbers. Choose an arbitrary point c in R.…

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.