Solve the differential equation dy/dx + 2y = e^x given that y(0)=1.
A box contains 3 red and 2 green balls. A ball is drawn at random and not replaced, and then another ball is drawn. Find the probability that the second ball drawn is red.
A manufacturer makes two types of gadgets, A and B. Each type A gadget requires 3 hours to produce, and each type B gadget requires 5 hours. If the total available production hours are 80, determine the maximum number of gadgets that can be produced.
Verify Rolle’s theorem for the function f(x) = x^2 – 4x + 3 on the interval [1,3].
A balloon is being inflated at a rate of 4cm^3/sec. Determine the rate at which the radius of the balloon increases when the radius is 2cm.
Evaluate lim(x->0) Sinx/x and explain why this is a fundamental limit in calculus.
Differentiate between addition and condensation polymers. Give examples of each type and mention two uses of polymers in daily life.
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