lim[(tanx-1)/x] as x->0. lim[ (1+sin(4x))^cot(x)] as x -> 0 from the positive side. lim[ [(a^(1/x) +...

lim[(tanx-1)/x] as x->0.

lim[ (1+sin(4x))^cot(x)] as x -> 0 from the positive side.

lim[ [(a^(1/x) + b^(1/x))/2]^x] as x -> infinity

Expert Solution

milcah answered 2 years ago

Evaluate the following limits using l'Hopital's rule. (a) lim x→0 (sin(x)−x)/(x^2) (b) lim x→0 (1/x) −...

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(a) Find the limit of the following functions: -lim as x approaches 0 (1-cos3(x)/x) -lim as x approaches 0 (sin(x)/2x) -lim as theta approaches 0 (tan (5theta)/theta) (b) Find the derivative of the following functions: -f(x) = cos (3x2-2x) -f(x) = cos3 (x2/1-x) (c) Determine the period of the following functions: -f(x) = 3 cos(x/2) -f(x)= 21+ 7 sin(2x+3)

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use laplace transforms to solve ivp x" + 4x' + 3x = 1, x'(0) = 2, x(0) = 1

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