For real number p, let f and g be defined by f(x) =e3 and g(x) = 1/xP, respectively, on [1,00). f(x) Show that lim = 0 for all p E R. x+0 g(x)

Q: Let X={1, 2, …, 16} and define function f(x)=rx for all x€X where rx is the remainder when 3x is…

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Q: For a function f: A --> B and subsets C and D of A and E and F of B, prove the following: f-1(E -…

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Q: b. Find lim (xv (xVx²+1-x²)

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Q: Consider the following piecewise-defined function: f(x) = { 4-ax² if x ≤1 b 2x if x > 1 Find the…

A: Ans :Now we need to sketch the graph in the interval [-3,3]Firstly let's find some points on the…

Q: Consider the following graph of the function g. From the given graph of g, state the numbers at…

A: The graph of a function g is given, to find its points of discontinuity.

Q: If f(x) = 5x – 4, then f(x) – f(-3) = 5. x +3 lim I-3 Select one: O True O False

A: Answer is true.  Using L hopital rule.

Q: Evaluate lim (tan-(t),e-2t,m²). t-1

A: We want to find given integral.

Q: 2. Let a, b be real numbers for which b > a. Let functions f,9,h be defined on a domain [a, b] in…

A: Solution is here

Q: Let f(x) = 2x2 +1. Evaluate f(4 + h) - f(4) lim h-0 h

A: Given, The function f(x)=2x2+1.

Q: 1 c) lim x+0 \ex-1 X.

A: the given expression is: limx→01ex-1-1x…

Q: Show whether f(x) is continuous (3х-2 f(x)={ x-2 x² -4 for x=- for x+ -

A: Given that, f(x) = 3x - 2; for x = - 2 f(x) = (x + 2)/(x^2 - 4); for x not equal to - 2 So when x is…

Q: Find lim h→0 lim h0 f(3+h)-f(3) h f(3+h)-f(3) h - if f(x)=x² +8. (Simplify your answer.)

A: To find the limit limh→0f(3+h)−f(3)h for the given function f(x)=x2+8, let's substitute the function…

Q: Find the domain of (fof)(x) if f(x)= 2 x+2

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Q: Let X={1, 2, --, 16} and define function f(x)=r, for all rE X where r, is the remainder when 3* is…

A: Let X=1,2,...,16 and define function fx=rx for all x∈X, where rx is the remainder when 3x is divided…

Q: Verify Rolle's theorem for the function 2x2 – 18x + 29 on the interval f(x) = [2, 7].

A: Given,          The function is fx=2x2-18x+29 on the interval 2,7.

Q: ) Evaluate the function  f(x) =x2   -(2x/1000 )for x=1,0.8,0.6,0.4,0.2,0.1 and 0.05 and guess the…

A: Given function, f(x)=x2-2x1000