Please answer ALL of the following ASAP I need a quick guide to the answer, I will be sure to leave a positive review if the questions are done both in a timely manner and neatly.

Question 1 (1 point) The derivative of a function f in terms of a limit is defined by which of the following? O lim f(h)-f(z) h-0 h O lim f(ath)-f(z) h O lim f(x)-f(a) r-a a O lim f(ath)-f(x) h-0 hQuestion 2 {1 point] The derivative can he used to find the: O a] point of intersection. O b) common factors. 0 c) instantaneous rate of change. 0 d) Both in and c are correct. Question 3 {1 point] A notation for derivative is: Question 4 (1 point) What is the derivative of h(x) = 42? ( a) o ( b) 42 O c) x O d) 42x Question 5 (1 point) In which quadrant is only the tangent ratio positive? O a) 1st Ob) 2nd O c) 3rd O d) 4thQuestion 6 {1 point] f (it?) = % can be written as: O a) fix} = x3"5 0 hr rm = xsrs O :1 rm = ears: 0 a} rm = m: Question 7 {1 point] Which rule would you use to differentiate HI} = sini3x}? O 3.] Sum rule 0 '33 Difference rule 0 5} Product rule 0 '3'} Chain rule \fQuestion 9-11 paint] Find the derivative of each of the fullewing functions. 1.y:5m43m2+7 2. f (3:) = 5643 3-901?) = :31} Blank # 1 Blank # 2 Blank # 3 \fAt time t (in days), the size S of a population of butterflies is given by the formula 600 S 1+ 49(0.6) Use the graph above and your knowledge of derivatives to answer the following: 1. What is the growth rate after 10 days? 2. When does the maximum growth rate occur? 3. Explain why the shape of the graph looks this way. Blank # 1 A/ Blank # 2 A Blank # 3 A/Question 11 (1 point) Carbon14 is a radioactive substance produced in the Earth's atmosphere and then absorbed by plants and animals on the surface of the earth. It has a halflife (the time it takes for half the amount of a sample to decay] of approximately 53"30 years. Using this known piece of information, scientists can date objects such as the Dead Sea Scrolls. The function N = Nmel't represents the exponential decay of a radioactive substance. N is the amount remaining after time t in years. N0 is the initial amount of the substance and h is the decay constant. 1. Find the rate of change of an initial amount of 1 gm of carbon14 found in the scrolls, if the decay constant is giyen as A = 1.21 x 104. 2. If the percentage of carbon14 atoms remaining in a sample is 739%. how old is the sample? Blank # 1 Blank # 2 Question 12 (1 point) A team of students seeks to make a flag representing their commitment to the earth. They will be using a green triangle inscribed in a yellow semicircle. Find the maximum area of the triangle inscribed in a semicircle of radius r