Give the domain of this function in interval notation

Reference no: EM132728617

Applied Mathematics assignment

1. Consider the function h(x)=4x/√(x^2-25)

(a) Give the domain of this function in interval notation.
(b) Use the appropriate limits to identify any vertical asymptotes. If none exist, write "None" and explain why.
(c) Use the appropriate limits to identify any horizontal asymptotes. If none exist, write "None" and explain why.
(d) Is the function's symmetry even, odd, or neither?

2. Evaluate the following limits

(a) lim 3/t - 3/(t² + t)
t→0

(b) lim | sin x|/sin x

x→0

θ→0

3. Consider the function g(x) = (√x-√5)/(x^2-6x+5)

(a) Give the domain of this function in interval notation.
(b) Evaluate lim-x→5??g(x)?.
(c) (8 points) The function g has a removable discontinuity at x = a. The discontinuity can be removed by creating a new function h(x)

h(x)= g(x), x≠a
=b, x=a

Use the definition of continuity of a function to find the values of the constants a and b.

4. Let g(x)=(x-1)/(x+1)

(a) Use the definition of derivative to find the slope of the tangent line to y = g(x) at x = 0. (b) Find the equation of the tangent line to y = g(x) at x = 0.
(c) Find the equation of the normal line to y = g(x) at x = 0.

5. Some unrelated, short answer questions.
(a) The limit lim-h→0??(?(1+h)?^10-1)/h? represents the derivative of some function f at some number a.
(i) Find a function f and a value for a. (ii) What is the value of the limit?
(b) Does x + tan x = 1 have a solution? Justify your answer.
(c) Sometimes a function f is not continuous on its domain but |f | is continuous, on the same domain.
Find an example of such a function f (i.e. f is not continuous at a point in its domain but |f | is).
Either sketch the graph of both |f | and f or find a formula that illustrates this.
(d) A factory manufactures metal cubes of volume V = 8000 cm3. An error tolerance of ±5 cm3 is allowed, which corresponds to a side length s between 19.996 and 20.004 cm. In terms of the formal definition of limx→a f (x) = L, identify x, a, f (x), L, δ, and E. No further explanation is necessary for this problem.

Reference no: EM132728617

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