Common Misconceptions (Calculus)

Calculus Misconceptions



f(x)=ex2,f(x) = e^{x^2},

what is the correct expression for f(x)?f'(x)?

Which statement(s) are true?

A. If f(x)=x2,f(x) = x^2, then f(x)=2x.f'(x) = 2x.

B. If f(x)=2x,f'(x) = 2x, then f(x)=x2.f(x) = x^2.

True or False?

Suppose ff is a differentiable function on the interval (a,b).(a,b). If ff is decreasing on (a,b),(a,b), then f<0f'<0 on (a,b).(a,b).

True or False?

111x2dx=x2+12+111=11=2.\displaystyle \int_{-1}^1 \frac{1}{x^2} \,dx = \left . \dfrac{x^{-2+1}}{-2+1} \right |_{-1}^1 = -1 -1 = -2.

True or False?

If f(x)=2x,f(x) = 2^x, then f(x)=x2x1.f'(x) = x\cdot 2^{x-1}.


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