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Essential Calculus: Early Transcendentals
- If a functionfis increasing on (a,b) and decreasing on (b,c) , then what can be said about the local extremum offon (a,c) ?arrow_forwardAssuming that lim x→a f(x)/(x−a)2 exists, find lim x→a f(x)/x-aarrow_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_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_forwardProve that lim ƒ(x) = L if and only if lim ƒ(h + c) = L. X->c H->0arrow_forwardProve that limx->∞ f(x) =lim t->0+ f(1/t) and limx->∞ f(x) =lim t->0- f(1/t) if these limits exists.arrow_forward