Calculus Questions

What is an equation of the line that passes through the point 4 4 and is parallel to the line 3x 4y 16

ind the distance between the two points in simplest radical form k 10 9 8 7 6 5 O T O 3 2 1 10 9 8 T 7 10 10 3 6 2 33 4 5 5 8 N 5 6 2 3 4 5 6 7 8 9 10

Determine the equation of the circle graphed below 12 11 10 96 8 76 7 6 54321 4 12 11 10 9 8 7 6 5 4 3 2 1 1 2 co 4 6 7 8 50 y 5 2 1 2 3 4 5 6 7 8 9 10 11 12 4 3

Find the length of the third side If necessary round to the nearest tenth 7 6

raph a line that is perpendicular to the given fine Determine the slope of the given line and the one you graphed in simplest to lick and drag on the graph to draw a line Click and drag to plot a perpendicular line The line will change colors when a parallel or perpendicular line is drawn accurately Answer Attempt 1 out of 2 TR 719 Ter 3

Write the quadratic equation in standard form 22 14 7r

An element with mass 490 grams decays by 28 6 per minute How much of the element is remaining after 16 minutes to the nearest 10th of a gram

Graph the inverse of the provided graph on the accompanying set of axes You must plot at least 5 points Click the graph to make a point Click it again to erase 10 9 8 7 6 5 4 3 2 y 10 1 9 8 7 6 5 4 3 2 1 1 2 3 5 8 10 1 2 3 4 5 6 7 8 9 10 X

Evaluate the function graphically O 10 9 8 7 6 5 4 3 2 1 10 9 8 7 6 5 4 2 1 1 2 3 4 y 56 7 8 9 10 1 2 3 4 5 6 7 8 9 10

ng along a gawa the relationship between distance and time Answer Attempt 1 out of 2 The independent variable x represents the variable is the on the So C 3 50 miles per hour Answer the questions below regarding V A function relating these variables is C x meaning after 3 because the and the dependent 2 number of miles traveled number of hours driving depends

f x 40 10 9 Step 1 Select a function then move with blue dot if necessary done v V 8 x 2 7 6 5 4 3 2 1 10 9 00 10 7 6 5 4 3 2 1 1 2 6 3 4 5 y 1 for x 4 for x 5 2 3 4 5 6 7 8 9 10

Under her cell phone plan Hawa pays a flat cost of 51 50 per month and 3 per gigabyte She wants to keep her bill at 64 10 per month Write and solve an equation which can be used to determine g the number of gigabytes of data Hawa can use while staying within her budget Answer Attempt 1 out of 2 Equation B

All exponential functions can be written in many forms Write the function f t 570 2 7 in the form f t ab Round all coefficients to four decimal places Answer Attempt 1 out of 2 t 15

Find the point on the graph of z 3x 3y2 at which vector n 12 18 1 is normal to the tangent plane P 2 3 14 A

Consider the partial derivatives Is there a function f which has these partial derivatives Yes If so what is it f 12x y Enter none if there is no such function any others Are there Yes y fz x y 5x y 6x y fy x y 4x5y 2x

z x y e ind dz dt using the chain rule Assume the variables are restricted to domains on which the functions are defined dz dt z 4t y 4 5

z ze Find 02 0u and 02 0e The variables are restricted to domains on which the functions are defined 02 0u 02 00 z u v u v

1 point Suppose z x sin y z 18 3t y 2st A Use the chain rule to find and as functions of x y s and t z 8s z Ot as B Find the numerical values of dz s 3 1 3 1 and when s t 3 1 dt

z x y e find az ou and az av The variables are restricted to domains on which the functions are defined z du 4 z dv x U y ln v

Let f x y z x y 2 and x s t y s t and z s t a Calculate the primary derivatives 3 4x y 2 dy af 2x y b Calculate dr 2st 2 as y as 2z 3s t 8 35 1 dz 8s c Use the Chain Rule to compute af 88 I S

1 x 3 x 5 Determine if the point 2 25 is on the graph of the function f x x Is the point on the graph of f x O Yes O No

b Given two polar curves 3 cos and 2 3 sin such that 0 0 2r i Find the intersection point s ii Sketch and on the same diagram iii Find the arc length of r that lies inside 2

Differentiate d dx y 6x 4 6x 4

Differentiate y 24 3 x x 24 dx 3 x x

Use the Chain Rule to calculate the partial derivatives g x y cos x y x u 4v y u v 8g du 94 ag du Express your answer in terms of the independent variables u v

Let f x 4 X a Find the derivative f x b Find f 2 a What is the first step in finding the derivative of f x O A Rewrite the function in the form f x OB Substitute x h for x in the original function OC Rewrite the function in the form f x rx OD Rewrite the function in the form f x x 1 Rewrite f x 4 X in this form f x 0 Which rule of derivatives should be used to differentiate functions of this form OA The rule that if f x ax then f x a OBThe rule that if f x mx b then f x m

Consider the partial derivatives s there a function f which has these partial derivatives Yes If so what is it Enter none if there is no such function Are there others any Yes v fz x y 5x y 6x y fy x y 4x y 22

Find the equation of the tangent plane to the surface determined by at z 3 y 5 1 x y z 60 0

Find the point on the graph of z 3x 3y at which vector n 12 18 1 is normal to the tangent plane P

Use the linear approximation of x y e x 2y at 0 0 to estimate f 0 01 0 02

10 Domain none 4 5 7 7 4 5 4 5 5 X 5 S 10 4 The given curve is the graph of a function of x by the Vertical Line Test The given curve is not the graph of a function of x by the Vertical Line Test 5 10 X

If z sin and x ln u and y v find the following partial derivatives using the chain rule Enter your answers as functions of u and v z

Find an equation of the tangent plane to the surface z 1x 3y 3x 3y 3 at the point 3 5 87 22 11

8g Use the Chain Rule to evaluate the partial derivative at the point r 0 2 2 4 80 where g x y 3 8g 80 r 0 2 2 1 8x 6y 11 x r sin 0 y r cos 0 7

Let f x y z x y z and x s t y s t and z s t a Calculate the primary derivatives of 32 dx 4x y dy 2x4y 38 38 af af 8z dx s b Calculate dy s dz as c Use the Chain Rule to compute af ds In eller 3

Find an equation of the tangent plane to the surface z 2 1x 3y 3x 3y 3 at the point 3 5 87

Find an equation of the tangent plane to the surface z 3y 5x at the point 3 1 42 2

Estimate f 2 01 1 97 given that f 2 2 2 fr 2 2 3 and fy 2 2 1 f 2 01 1 97

Find the second partial derivatives of the function f x y x y 5x y a f x 1 2 3 4 8 f y x 8 f dxdy a f dy Chalk

Find the equation of the tangent plane to at the point 0 2 11 2 z e y

Calculate all four second order partial derivatives and check that fay fyr Assume the variables are restricted to a domain on which the function is defined f x y 4 sin 2x cos 6y fyy 8 9

Evaluate the function at the specified points h x y z xy 4 3 2 3 2 2 At 4 3 2 At 3 2 2

Derive the formula for the volume of a right circular cone of height h and radius r using an appropriate solid of revolution The volume of the solid generated by revolving the region between the x axis and the graph of a continuous function y f x 20 Lsasx b radius height about a vertical line x Lis V 2 2x the volume of a right circular cone shell shell dx This is known as the shell method How can the shell method be used to fin O A Rotate a shell in the shape of a quarter circle with radius r about the y axis OB Rotate a shell in the shape of a triangle with height h and base radius r about the y axis OC Rotate a shell in the shape of a rectangle with height h and base b about the y axis

Calculate all four second order partial derivatives of f x y 3x y 7xy fax x y fry x y fyr x y fyy x y I 9 9

Find the partial derivative indicated Assume the variables are restricted to a domain on which the function is defined z sin 7x y 4xy

Suppose f x y xy 3 Compute the following values f 5 4 f 4 5 f 0 0 f 2 4 f x 5 f 4 y f t 4t f uv u v 12 8

6 To reach Platinum Medallion status with Delta Airlines you need to fly at least 75 000 miles but less than 125 000 miles in a given year Express the set of annual miles you could earn x to get Platinum status in algebraic interval and set notation

7 Kalia is planning the transportation for the senior trip The number of students in the senior class is 463 but the trip is entirely voluntary If each bus can seat 48 students describe the set of the number of busses b they may need in set notation

9 Use algebraic and interval notation to describe all possible values of a so that 2 81

10 Which of the following statements is true about the set of real numbers described by the interval 15 1 A This set contains only one point x 15 y 1 B This set includes all real numbers between 15 and 1 not including 15 and 1 C This set is equivalent to the set given by 14 1 D 15 is not included in the set but a 1 is included