A) Write a difference quotient that best approximates the instantaneous rate of change of g at x=2.5. (b) Let h be the function defined by h(x)=g(f(x)). Find the value of limx→3h(x) or explain why the limit does not exist. Use correct limit notation in your answer.

(c) Let k be the function defined by k(x)=(4−f(x))g(x). Consider x=2 and x=4. Determine whether k is continuous at each of these values. Justify your answers using correct limit notation.

Please show all your work!!

Find the value of 1715⋅211.though these numbers aren't quite as nice as the ones from the example or the previous part, the procedure is the same, so this is really no more difficult. give the numerator followed by the denominator, separated by a comma.

Aspacecraft can attain a stable orbit 300 kilometers above earth if it reaches a velocity of 7.7 kilometers per second. the formula for a rocket's maximum velocity v in kilometers per second is vequalsminus0.0098tplusc ln upper r, where t is the firing time in seconds, c is the velocity of the exhaust in kilometers per second, and r is the ratio of the mass of the rocket filled with fuel to the mass of the rocket without fuel. find the velocity of a spacecraft whose booster rocket has a mass ratio of 20, an exhaust velocity of 2.1 km/s, and a firing time of 15 s. can the spacecraft achieve a stable orbit 300 km above earth?

What should be done to both sides of the equation in order to solve -5m = -40? a) multiply by -5. b) divide by -5. c) multiply by -40. d) divide by -40.