Which of these properties are true? Which properties of limits are true. Choose

Question

Which of these properties are true?

Which properties of limits are true. Choose all that apply. {Assume u = f(x), v = g(x), and k is a real number) lim_x rightarrow c(uv) = (lim_x rightarrow c u) (lim_x rightarrow c v) lim_x rightarrow c(u - v) = (lim_x rightarrow c u) - (lim_x rightarrow c v) lim_x rightarrow c(u^2) = (lim_x rightarrow c squareroot u) lim_x rightarrow c (ku) = k(lim_x rightarrow c u) lim_x rightarrow c (u/v) = u/v lim_x rightarrow c (k) = c lim_x rightarrow c x = c lim_x rightarrow c (x^n) = c^n

Explanation / Answer

limit satisfies addition, substraction, multiplication. hence 1st, 2nd are true.

3rd is false as lhs and rhs are completely different.

4th is true as you already ticked.

5th is wrong. rhs =u/v is still function of x whereas lhs is independent odf x as value of x is put there through limit.

k is independent of x . so lim x tend c(k)=k so 6th is wrong also.

7th is right

8th is right

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