The function H : R → R defined by 1, if 120 0, if r<0 H(x) =

Q: 1 1r

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Q: If f"(x)>0 on an interval I then...

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Q: If f is even, then f' is even.

A: The question is taken from the function in which we have to do that f is even then its derivative is…

Q: Set f(x) = In(9x - 8). Question 1 For k > 1, f (k) (1) =

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Q: A. Consider the function defined by [x² +1, if x<5 f (x)={ |6x– 4, if x25 a. Is f continuous at x =…

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Q: Use the Mean Value Theorem to show that there is no function f satisfying f(0) = 0, f(9) = 5, and…

A: If function continuous on a,b and differentiable on a,b such that fb≠fb Then f'c=fb-fab-a

Q: (c) Show that f(x)>0 for all values of x, x # -2.

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Q: Determine L[f]if 0, f(1) = {1- 1, 0 2. 1,

A: Given that, A function f(t), t ≥ 0, its Laplace transform F(s) = L{f(t)} is defined as

Q: o Function f₁: R → R is defined by f₁ (x) = (x + 1)². • Function f2: R → R is defined by f2(x) =…

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Q: Let x2-2x-3 f(x) = キ3 if For what Values of x is f Contin uo4s? Find the absolate min values of the…

A: Given function is

Q: From algebraic form of function ez, prove that  |ez| = ex

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Q: What is the domain for f (æ) = Væ – 3.

A: Given fx=x-3

Q: 7. Find the function U, whose first difference is *C

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Q: 6. Prove that f(x)=√x is continuous for all x ≥ 0.

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Q: Choose a prime number, n, between 10 and 99, and using n, prove why the function ƒ(e (2πix)/n )=…

A: G is the group of nth roots of unity under complex multiplication.Zn is the group of integers mod n…

Q: Solve the following initial value problems using the Laplace Transform. You may use Mathematica to…

A: Since you have posted multiple question in this question which are not interlinked so i have solved…

Q: Let f(x) = x³ – 6, – 3 < x < - 1 The domain of f- is the interval [A, B 1 where A and B = %3D

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Q: Find a point c satisfying the conclusion of the MVT for the following function and interval: f(x) =…

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Q: If a < c < b and f(c) is the greatest value on the interval (a, b), then f(c) is a ....

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Equations and Inequations

Equations and inequalities describe the relationship between two mathematical expressions.

Linear Functions

A linear function can just be a constant, or it can be the constant multiplied with the variable like x or y. If the variables are of the form, x2, x1/2 or y2 it is not linear. The exponent over the variables should always be 1.