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Calculus (MindTap Course List)
- Determine value for c so that lim f(x) x--> 3 exists f(x)= 1/3x+c For x<3 -x+8 For x>3arrow_forwardDefine what it means to say that lim g(x) = k. X->0arrow_forwardSuppose that a function ƒ(x) is defined for all real values of x except x = c. Can anything be said about the existence of limxSc ƒ(x)? Give reasons for your answer.arrow_forward
- Give an example where lim x → 0 ( f ( x ) + g ( x ) ) exists but neither lim x → 0 f ( x ) nor lim x → 0 g ( x ) exists.arrow_forwardSuppose X⊆ R, a ∈ X', f,g : X -> R, lim {x -> a} f(x) = L, and lim {x -> a} g(x) = M. Use he definition of limit of a function to prove lim {x-> a} f(x) + g(x) = L + M.arrow_forwardprove that lim x-2 f(x)=4 if f(x)= x^2, x does not =2 1 , x=2arrow_forward
- Suppose that a function ƒ(x) is defined for all real values of x except x = c. Can anything be said about the existence of lim x approaches c ƒ(x)? Give reasons for your answer.arrow_forwardProve that if the limit of f(x) as x approaches c exists, then the limit must be unique. ( Hint: Let lim f(x) = L1 as x approaches x and Lim f(x) = L2 as x approaches c and prove that L1=L2.arrow_forwardWhat is a limit, and what does it mean to say: lim f(x)=1? x->7-arrow_forward
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