Calculus Questions

Given f x 6x and g x 4x 6 evaluate the following expressions a fog 4 b gof 2 c fof 1 d gog 0 a fo g 4 420 Simplify your answer b gof 2 582 Simplify your answer c f of 1 Simplify your answer

Integral 7 O secz tan a

Evaluate OF f x dx where f x 62 T I 7 sin x 0 I T

Evaluate the indefinite integral 4 2 6 7 2 1 d dx C

Evaluate the indefinite integral 6x4 75 3 dr C

If f x f x 14 H t dt then

T 4 7 cos u BUJ 16 du

Compute the indefinite integral 1 sin cos z

Evaluate the indefinite integral 224 47 dx C

Evaluate the integral

Evaluate the indefinite integral 8 dx C

13 4 i Let f x sin x 3 3x with xe 1 1 Given 0 1 find a 8 0 such that for all x y 1 1 if x y d then f x f y 0 1 E ii Consider x dx where f is as in part i The partition Pn cuts 1 1 into n equal pieces For what n we have U f P L f Pn 0 01 lot t

1 Use the graph of y f x to sketch the graph of its derivative f x 20 16 124 8 4 0 4 8 12 16 20 2 3 A 5 4 3 1 1 34 3 2 O T 2 3 4 in M 3 4

astontbooco 65 What happens to the graph of the function y f x if you make these changes to its equation a replace x with x 8 b replace y with y 2 c replace x with x 4 and y with y 7

21 Find the center and radius for the circle a x 2 y 3 16 b x y 3 25

1 Describe how the graphs of the following functions relate to the graph of y f x b y f x 7 c y f x 4 4 a y f x 9 Xxx s d y 6 f x e y 3 f x 5 f y 2 f x 3 10

O 6 5 b f x x 2 x 5 3 O f x x 2 x 5 O f x x 2 x 5 O f x x 2 x 5 2 T 7 6 5 4 3 2 1 1 2 3 4 Shift Mouse Wheel to zoom Shift Mouse Drag to pan 5 3 X x

Suppose h x f g x Given the table of values below determine h 1 f x g x f x g x 3 2 7 10 6 4 6 3 5 5 1 in your answer X 1 2 4 5 7

Find the derivative of y O Select the correct answer below O O 3x 30x 25x 5 6x x 25x 5e x 6x 1 2 A 25x e x x 1 25x 5x

Determine s x if s x ln 4x 5x 2x 5 Select the correct answer below 12x 10x 2 4x 5x 2x 5 O 1 O 4x 5x 2x 5 12x 10x 2 O In 4x3 5x 2x 5 O In 12x 10x 2 4x 5x 2x 5 12r 10x 2

The slope field for the equation dP dt 0 0333333P 30 P for P20 is shown below 21 1 1 717 11 11 11111 38 On a print out of this slope field sketch the solutions that pass through 0 0 3 12 12 3 14 5 3 6 36 and 6 30 For which positive values of P are the solutions increasing Increasing for Give your answer as an interval or list of intervals e g if P is increasing between 1 and 5 and between 7 and infinity enter 1 5 7 Inf For what positive values of P are the solutions decreasing Decreasing for Again give your answer as an interval or list of intervals e g if P is decreasing between 1 and 5 and between 7 and infinity enter 1 5 7 Inf What is the equation of the solution to this differential equation that passes through 0 0 P 0 If the solution passes through a value of P 0 what is the limiting value of Past gets large

Find the derivative of the function y xe Select the correct answer below O e 2x 1 O e x 2x O e x 1 O 2xe x 2x PLA

Determine s x if s x ln 4x3 5x 2x 5

If t x Select the correct answer below O 0 04e In x O O t x 0 04 what is t x O In x es e t x 0 04 t x In x In ln x e In x In x xex 1 e In x t x 0 04 0 04e 1 I

What is f x if f x 40x p

Find the domain and range of the function f x 3x 18x 34 O A Domain 00 00 Range 7 00 OB Domain 0 00 Range 0 0 OC Domain 0 00 Range 0 3 O D Domain 00 00 Range 0 00

Consider the logistic equation y y 1 y a Find the solution satisfying y 0 16 and y2 0 5 3 t Y2 t b Find the time t when y t 8 t c When does y2 t become infinite

Use Euler s method with step size 0 25 to compute the approximate y values 31 32 33 and y4 of the solution of the initial value problem Y1 Y2 Y3 20 11 y 2 5x 2y y 1 5

Using separation of variables solve the differential equation dy 10 x dx Use C to represent the arbitrary constant 11 Y

Find an equation of the form y f x for a curve with z intercept 0 whose tangent line at any point z y has slope ze

Find the solution to satisfying dy dt 2y y 4 3

Match each differential equation to a function which is a solution FUNCTIONS A y 3x x B y e 8 C y sin x D y x E y 6 exp 2x DIFFERENTIAL EQUATIONS 1 2x2y 3xy y 2 y y 0 3 y 15y 56y 0 4 xy y x

Graph the piecewise function to find the domain and range Give the answers in interval notation f x 2x 3 if x 0 3x 4 if x 0 Domain inf inf Range help intervals help intervals

The surface given in spherical coordinates as cos p p is a cylinder

3 Answer Write the definitions of sin 0 andcos 0 using the limit definition of derivative de 2512 X126

Ben and Evan start from Listowel and drive along perpendicular roads Ben drives at a speed of 45 km h and Evan travels at a speed of 40 km h ok it was icy If Evan begins one hour before Ben at what rate are their cars separating three hours after Evan leaves olesworth Bowling E B Palmerston Norgan theatre

he local and absolute extreme values of f r s c d P q a b Q Give the local extreme values of f Choose correct answer below OA There is no local extrema O B Local minima are q and s local max are b and d O C Local minima are b and d local maxima are q and s Give the absolute extreme values of f Choos correct answer below OA Absolute minimum is q OB Absolute minimum value is b OC There is no absolute extreme value

determine which function matches the graph Which function matches the graph OA f x 2x 2x 2x 2x 2 OB f x 2x 2x 2x 2x 2 OC f x 2x 2x 2x 2 OD f x 2x 2x 2x 2 40

Give the equation of the function whose graph is described The graph of y x is shifted 3 units to the left This graph is then vertically stretched by a factor of 5 and r across the x axis Finally the graph is shifted 7 units downward OA y 5 x 3 7 OB y 5 x 3 7 O c y 5 x 3 7 OD y 5 x 7 3

X 6 x 2 7 OA 1 5 OB 5 1 OC 6 2 OD 2 6 zero product property

ive a formula for a piecewise defined function f for the raph shown An too Q OA f x OB f x Oc f x OD f x 2 if x 0 x 6 ifx20 2 ifx 0 x 6 if x 0 2 if x 0 x 6 ifx20 2 if x 0 x if x20

termine if the graph is symmetric with respect to the axis y axis or origin 27 Q OA Origin OB X axis OC Y axis OD No symmetry

h x 1 2 x 8 OA f x g x x 8 OB f x x g x x 8 OC f x g x x 8 OD 1 x g x x 100

rm the indicated operation Write the result in standare 3 2i 6 61 A 30 6i OB 12 6i 18 OC 30 6i OD 6 30i

For the following exercise solve the rational exponen x x 6x 6x 0 23 x Question Help VIDEO Written Example Post to forum Submit

Scribe Alara shitag Xinyi Boys 7 Short of a formal proof how could you convince someone that lim h 0 8 Apply the limits above to find sin 0 and cos 0 Answer Alara Shitao Baji Scribe Xinyi Aleve Shides Bezi two J sint VI SIVE sin h h O f1 49 1 and lim h 0 hi c nh h Sin la ht h 0 1 h 6 suth k hae ni coshti sah 40

Question 12 Use the distributive law to find the product 26 1 6 1

Factor out the smallest power from each expression Wr a 5 3a a

Find f 4 for f x given below 4x 1 if x 4 f x 4x if 4 x 6 4 3x if x 6 OA 5 OB 8 O C 16

Solve the inequality analytically writing the solution set in interval n 10 4x 72 5x 8 OA 4 OB 9 00 OC 0 9 OD 4 00