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Over what intervals are the following functions continuous? Justify your answer using the definition of continuity.
a. h(x) = sin (x2)
b. k(x) = 1 / (√(x2 + 7) - 4)
Let f and g be twice differentiable functions such that f'(x) ≤ 0 for all x in the domain of f. If h(x) = f(g(x)) and h'(2) = 4. What (if anything) can you say about f, g, and h at x = 2?
The quantities ai in this exercise are all positive real numbers. Show that a1a2 ≤(a1 + a2/2)2.
Evaluate the polynomial x^2+ 2y^2- 3xy for x = 3 and y = 4. Solve the problem. Show all steps necessary to arrive at your solution. Find a polynomial for the sum of the areas of these circles.
When is it necessary to find the least common denominator (LCD) of two rational expressions? Describe, in your own words, the process for finding the LCD of two rational expressions. How is factoring related to this process?
A rational expression is a fraction of two polynomials. If you need to add or subtract two rational expressions, how would you do it?
Elementary row operations.
In 1920, the record for a certain race was 45.4 sec. In 1960, it was 44.6sec. Let R(t)= the record in the race and t= the number of years since 1920. Find a linear function that fits the data.
Find the exact value of tan (α - β), cos 2α, and sin β/2 under the given conditions: cos α =√5/5, 0
dominic arrived at work and went behind the counter at the north end. as he faced out over the counter north was to his
Solve the inequality
In solving an equation involving radicals, it is sometimes necessary to square each side of the equation. But doing this can introduce extraneous roots, which do not satisfy the original equation.
Add and simplify (5-2i) + (8-6i) = Type answer in form a+bi
The length of a rectangular parking lot is 40 ft more than the width. If the parking lot is iv feet wide, express its area as a function of the width.
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