Differentiation Questions and Answers

Find fxy for f x y 8x y 7y 2x 24x 48xy 28 14

Find the partial derivative Find fz 4 4 when f x y 7x O 32 92 20 20 9xy

4 Write your answer as a fraction or as a whole or mixed numb

The partial fraction decomposition of where f x g x Question Help Video Message instructor 8 x 4 Submit Question can be written in the form of f x g x 2 2 2 2

Find the domain of function k x 18 3x Write your answer using interval notation in the box below Enter your values as integers or reduced fractions Domain of k x 18 3x x Question Help Video Message instructor

Solve the given inequality Enter your answer using interval notation and exact values 3k 5 5k 6

Write the expression A cos 0 B sin 0 OB OD OC csc 0 sec 0 as a single term C tan 0 D cot 0

1 CSC 0 O cos 0 sin 0 O cos 0 sin

1 All answers listed O sin cos 0 Ocsc 0 cot 0 O sec 0 tan 0

sec sin 6 cos 8 1 sin 8 1 cos 8 cos sin 0

Simplify to a single trig function with no denominator cot 0 sec 0

Simplify to a single trig function with no denominator tan 0 sec 0

For the function 1 f x 4 3x 4 lim f x I 4 if if x 4 if 4 x 0 x 4 use algebra to find each of the following limits lim x I 4 lim f x I 4 For each enter DNE if the limit does not exist Sketch a graph of f x to confirm your answers

4 3 2 1 5 4 3 2 1 2 3 lim f x I 3 lim f x I 3 f 3 lim f x I 3 1 a Determine the following values Enter DNE if a value does not exist enter oo lower case o if the limit approaches positive infinity or oo if the limit ap aches negative infinity Q 2 3 4

1 point The population of a colony of rabbits grows exponentially The colony begins with 10 rabbits 5 years later there are 380 rabbits a Express the population of the colony of rabbits P as a function of time t in years P t b Use the graph to estimate how long it takes for the population of rabbits to reach 1000 rabbits It will take years round to nearest 0 01 year

Fill in the blanks with the correct values 0 047 kg g mg 0 047 kg g mg Simplify your answer Type a whole number or a decimal

Fill in the blanks with the correct values L KL 49 mL L KL 49 mL

Find the measure of Zx in the figure The measure of Zx is 55d

Perform the conversion 92 mL CC CC 92 mL Type a whole number or a decimal

3 1 pounds ounces 3 1 pounds ounces Round to one decimal place

Divide in the indicated base 35 2315 5 R 15

Divide in the indicated base 56 4516 R

15 feet inches 15 feet inches Type a whole number or a decima

10 5 10 5 0 10 5 10 K 5 5 0 5 10 5 What is k D 5

For the function f x xt3 find fixth f x h

Add in the indicated base 1245 445 1245 445 15

Estimate the value of the limit to at least 2 decimal places r 14x 48 7x 56 lim I 8 SUAJSE

Determine lim csc x cot x 0 1 0 8 1

Determine the tangent line to the ellipse2 1 at the point 2 5 Oy Y Y5 x Oy 5 4 5 X 10 none of these y Yox 10 y 10 x 4 5 5 Yo 5

Determine the equation of the tangent line to the curvex y 4 at the point 3 3 1 The curve is called an asteroid Oy x 1 y Oy x 4 Oy x 4 Oy x 4 y x 4 3

Calculate y for xy5 x y x 3y 1 y5 4x y 5xy x4 3 O yl yl y 4xy 4xy x 1 y5 2x4 yl 5xy x 3 yl xy 3x 3 g3 5 1

1001 four 211 four The difference is 790 four Simplify your answer

Suppose that F x f g x and g 14 2 g 14 5 f 14 15 and f 2 16 Determine F 14 24 20 140 17 80 Question 4 0 5 points Listen

If f x 6 cos x sin x determine f x and f x f x 6 sin x sin 2x f x 6 cos x cos 2x Of x 6 sin x cos x f x 6 cos x 2 cos x sin x Of x 6 sin x sin 2x f x 6 cos x 2 cos 2x f x 6 sin 2x sin x fll r 6 cos 2x 2 cos x

Subtract in the indicated base 11234 1334 11234 1334

Add in the indicated base A69412 137B12 A69412 137B12

If a cylindrical tank holds 10 000 gallons of water which can be drained from the bottom of the tank in an hour then Torricelli s Law gives the volume of water remaining in the tank after t minutes as 1 2 v t 10000 1 t 0 t 60 Determine the rate at which 60 the water is flowing out of the tank the instantaneous rate of change with respect to t as a function of t OVI t 1000 50 t OVI t 1000 50 t 3 OVI t 50 t t 1000 50 t

Use the definition of the derivative to determine f x for f x O O O O O 2 3 2x 1 2 2x 1 1 1 3 2x 1 2 1 3 2x 1 2 1 1 2x 1 1 2x 1

Use the definition of the derivative to determine f 3 where f x x 2x 25 27 25 18 Does not exist Question 6 0 5 points Listen

Listen Determine the slope of the tangent line to the curve y 5x 4 40 40 4 25 at the point 4 22

Differentiatey O y cos x 4sin x yl tan x 4 sec x yl sec x tan x sec x 4sec x tan x sec x Oy cos x 4sin x sec vall sec ix 48ec i vall i 3 sec x Oy cos x 4sin x X COS x 4sin x

Add in the indicated base 3367 5557 3367 5557

Answer the questions about the following function f x x 12 x 3 a Is the point 5 6 on the graph of f b If x 2 what is f x What point is on the graph of f c If f x 2 what is x What point s is are on the graph of f d What is the domain of f e List the x intercepts if any of the graph of f f List the y intercept if there is one of the graph of f 18 2 Simplify your answer Type an ordered pair Use a comma to separate answers as needed d What is the domain off The domain is Type your answer in interval notation e List the x intercept s if any of the graph of f Select the correct choice below and if necessary fill in the answer box to complete your choice OA The x intercept s is are Type an integer or a simplified fraction Use a comma to separate answers as needed OB There are no x intercepts f List the y intercept if any of the graph of f Select the correct choice below and if necessary fill in the answer box to complete your choice OA The y intercept s is are Type an integer or a simplified fraction Use a comma to separate answers as needed

Solve the following inequality algebraically Express your answer using set notation or interval notation Graph the solution set Verify your results using a graphing utility 4x 8213 X Express the solution in interval notation Select the correct choice below and if necessary fill in the answer box to complete your choice OA The solution set is Type your answer in interval notation Use integers or fractions for any numbers in the expression OB The solution is the empty set Graph the solutions set Choose the correct graph below OA 12 Oc 12 OE HHH 12 9 9 6 3 6 9 6 0 3 0 3 0 3 3 73 6 6 6 9 12 9 9 12 12 B OD OF 12 9 6 3 H H 12 9 6 0 3 0 12 9 6 3 0 3 3 3 6 6 6 9 9 9 12 12 12

Draw a complete graph so that it has y axis symmetry 0 3 2 1 Choose the correct graph below O A O C 5 B O D

10 8 2 N 4 2 6 8 10 Clear All Draw Dot Line Segment 12 a Mark the two points on the graph that are needed to calculate Average Rate of Change over the interval 1 3 b Connect the points with a line segment c The Average Rate of Change over 1 3 is

Given the points 8 8 and 6 1 find the rate of change between the points Answer Round to three 3 decimal places

Suppose that an object is moving along a vertical line Its vertical position is given by the equation L t t 2t 5 where distance is measured in meters and time in seconds Find the approximate value of the average velocity accurate up to three or more decimal places in the given time intervals between t 5 s and t 12 s Vavg

Answer the questions about the following function f x X 10 X 2 a is the point 5 4 on the graph of f b If x 1 what is f x What point is on the graph of f c If f x 2 what is x What point s is are on the graph of f d What is the domain of f e List the x intercepts if any of the graph of f f List the y intercept if there is one of the graph of f a Choose the correct answer below OA Yes because substituting x 4 into the given equation results in 5 B Yes because substituting x 5 into the given equation results in 4 c No because substituting x 5 into the given equation does not result in 4 D No because substituting x 4 into the given equation does not result in 5 b If x 1 f x Simplify your answer

Convert the numeral to a numeral in base 10 20712 20712 10