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Show whether the following functions are uniformly continuous on the given domain.
1. F(x)=x^3 on [-1,1]
2. F(x)= 2x/2x-1 on [1, infinity]
3. F(x)= sinx/x on (0,1)
4. F(x)= 1/x on (0,1)
1,2,3,4,5;the abcissa is two less than the ordinate.What is the domain and range
Is the term (x+2) a factor of the polynomial shown below? f(x)=x^4+5x^3+10x^2+20x+24
Integral of sin(x^2)
Determine the interval of convergence for the power series
"\\displaystyle\\sum_{n=1}^ \u221e" 3n(x-1)n/(n+1)2
Determine for which value of "\\alpha" the given series converge absolutely, converge conditionally, or diverges.
- "\\displaystyle\\sum_{k=1}^ \u221e ((-1)" k+1 * "\\alpha^k" ) / k2
- "\\displaystyle\\sum_{k=1}^ \u221e ((\\alpha -1)^k\n\n\u200b" ) / k
For each of the following series, determine whether it is absolutely convergent, conditionally convergent, or divergent. Justify your answer.
- "\\displaystyle\\sum_{n=2}^ \u221e (-1)^n\/(n ln n)"
Find the integral surface of the equation x2p+y2q+z2=0 passing through z=1,x+y=xy
Answer with chain rule
Z = cos (x² + y²), x = u cos v, y = u sin v
(1) If the total cost of a firm is c(x) = 1.5x^3 - 5x^2 + 20x + 5 . Find the marginal cost (in dollars) when 25 units are produced and sold. Where did you get the 3?
What use does Calculus have in the real world? Describe what part calculus plays in the real world with examples.
