4 Statements
Calculus
Level
5
Which of the following statements are true?
- All continuous functions have an antiderivative .
- Every differentiable function that has an inverse has a differentiable inverse.
- The terms of a convergent series can never be arranged into a divergent series.
- Every polar function has a parametric equivalent.
3,4
4
2,3
3
1,2
2
1
1,4
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1 solution
Statement 1: True because by FTC, every continuous function has a definite integral that can be a function of X. Even if the antiderivative cannot be expressed in terms of polynomial or transcendental functions, it exists and has numeric values.
Statement 2: False because a horizontal tangent on a differentiable function is a vertical tangent on its inverse.
Statement 3: False because it is only true if the series converges absolutely.
Statement 4: True because by definition, a polar curve r(t) can be defined by the equations x = rcost and y = rsint