Application of derivatives Questions and Answers

Find the derivative of the given function dx 3 y 8 cos x

Find the derivative of the given function V 20 tan s 1 dV ds Type an exact answer using radicals as needed

Find the derivative of the given function r sin 30 dr Type an exact answer using a pooded

Find the derivative of the function by using the product rule Then multiply out the function and find the derivative by treating the function as a polynomial Compare the results y 5x 4 2 x ax ax d d 2 x 5x 4 5x 4 dx 2 x dx 5x 4 2 d d 2 x 2 x 5x 4 dx dx D 5x 4 2 The derivative using the product rule is y 14 10x Multiplying the function out results in the polynomial 5x 14x 8 Simplify your answer Do not factor The derivative of the polynomial is y 10x 14 Compare the results Choose the correct answer below OA The derivatives found by both methods are the same OB The derivatives found by both methods are negative inverses

Find the derivative of the given function y 3sin 3x4 5 dx

Find the second derivative f x 5x 3

Find the derivative of the function by using the quotient rule 4x 1 x 9 2 y y

Evaluate the derivatives of the given function for the given value of x Check your results using the derivative evaluation feature of a graphing cal y 4x 5x 4 3 x 5x x 0 0 I C a fraction

Find the derivative dy 10x 7 3 2 y

If the following function is continuous what is the value of a b 3t 2t 1 h t A 2 OB 4 OC 0 OD 1 E 3 ift 0 a cos t b if 0 t 3 ift 2 4 sin t

If g x is continuous for all real numbers and g 3 1 g 4 2 which of the following are necessarily true I g x 1 at least once II lim g x g 3 5 x 3 5 III lim g x lim g x x 3 x 3 OA I only OB II only C I and II only D I II and III E None of these

Let f be defined as follows where a 0 x x 2ax a xia 5 ifx a Which of the following are true about f I lim f x exists x a II f a exists III f x is continuous at x a A None ifx a OB I II and III O C I only OD II only OE I and II only

6 8 6 9 6 99 7 01 7 1 7 2 g x 9 44 10 21 10 92 11 08 11 31 12 56 X It would appear that lim g x x 7 OA 11 OB Does not exist OC X 4 O D O E 7

Find the general antiderivative of f x 2x 1 6 3 x2 x

lim 818 12 2 3x 4 O A 0 O O B 2 OC 2 D 3 OE 3

Which of the following is an even function NAVA Graph I Graph III Graph II Click here for long description A I only B II only C Ill only D I and III only

Write the arithmetic sequence 17 23 29 35 in the standard form an

Online Retail Sales Since the inception of the Web online commerce has enjoyed phenomenal growth But growth led by such major sectors as books tickets and office supplies expected to slow in the coming years The projected growth of online retail sales is given by R t 12 24e 0 136t 0 t 4 where t is measured in years with t 0 corresponding to 2007 and R t is measured in billions of dollars per year Online retail sales in 2007 were 116 billion a Find an expression for online retail sales in year t s t b If the projection held true what were online retail sales in 2011 Round your answer to the nearest integer Enter your answer in billions of dollars billion

3 Find equations of all lines having slope 3 that are tangent to the curve y x 5 Select the correct choice below and fill in the answer box es within your choice OA There are two lines tangent to the curve with a slope of 3 The equation of the line with larger y intercept is and the equation of the line with the smaller y intercept is Type equations

Find the following for the vectors v 6i 5k and u i j k a v u v ul b the cosine of the angle between v and u c the scalar component of u in the direction of v d the vector proj u 1 1 Type an exact answer using radicals as needed u 3 Type an exact answer using radicals as needed 1 183 b The cosine of the angle between v and u is Type an exact answer using radicals as needed 1 61 c The scalar component of u in the direction of v is Type an exact answer using radicals as needed d proj u Type your answer in terms of i j and k Type an exact answer using radicals as needed

Find equations of all lines having slope 2 that are tangent to 18 the curve y X 4

cylindrical coordinate integral 0 The value is Type an exact answer using as needed r dz dr de

X The equation r t 3 cos t i 3 sin t j 9t k is the position of a particle in space at time t Find the particle s velocity and acceleration vectors Then write the particle s velocity at t product of its speed and direction 2 The velocity vector is v t The acceleration vector is a t The velocity vector at t written as a product of the speed and direction is 1 00 Type exact answers using radicals as needed as a

Given that the polynomial f x has 9 x intercepts which of the following most accurately describes the degree of f x Select the correct answer below The degree of f x is at most 8 The degree of f x is at least 10 The degree of f x is at most 9 O The degree of f x is at least 8 The degree of f x is at least 9 The degree of f x is at most 10

Given that csc x 2 6 what is csc x

Given that csc x 2 what is csc x

2 Drag the black dot to shift your graph in the desired direction Use the blue draggable dot to change the period Drag the orange dot to change the amplitude and or reflect with respect to the x axis The horizontal distance between the vertical dotted green lines corresponds to one period Provide your answer below 2TT 11 31 2 2 1 0 0 2T 0 23T 3 41

Given that csc x 7 what is csc x

Analyze and sketch a graph of the function Identify any relative extrema points of inflection and asymptotes Use a graphing utility to verify your results If an answer does not exist enter DNE f x arccos maximum minimum point of inflection horizontal asymptote vertical asymptote x y x y x y 0000

The system of differential equations has a general solution where Re eta x t Re etb Re etc Im eta x t Im e b Im etc x 3 9 9 0 1 4 1 2 x 1 x t c x t C x 1 C3x3 t

The matrix A det 9 9 3 1 2 a11 a12 921 a31 0 1 2 4 V a13 922 a23 932 a33 1 2 1 2 9 a 1 2 b 2 c 0 9 a 4 b 1 2 c 0 which is the system a a b b where b The eigenvalue with positive imaginary part is For eigenvalue A the eigenvector has components a b and c that satisfy 3 a 0 b 1 c 0 i a b 301 9 12 9 4 1 2 has characteristic equation b i b 0 Choosing the first component of the eigenvector as a 1 this eigenvector is a 13 18 c 0 c 0 i c 0 i and c 27 i

The matrix A det 3 A 4 2 3 2 a11 a12 921 922 3 2 3 2 4 2 a 2x a 2 4 a 32 b 0 which is the system c 2 c 4 c 32 d 0 which is the system The eigenvalues are For eigenvalue 2 the eigenvector has components a and b that satisfy 3 a 2 b 0 For the eigenvector is G a 4 3 N b 0 b 0 For eigenvalue 22 the eigenvector has components c and d that satisfy 32 c 2 d 0 0 d 0 d 0 has characteristic equation

Question Given that cos 0 necessary Brovide swer below and is in Quadrant III what is sin 0 Give your answer as an exact fraction with a

Use trigonometric ratios to determine the length of x in the right triangle below X 71 5 cm Round your answer to the nearest tenth and do not include x or the units in your answer Just enter the numeric value

d y Find an equation for the line tangent to the curve at the point defined by the given value of t Also find the value of dx T x 8 sint y 8 cost t 4 represents the line tangent to the curve at t 4 The equation Type an exact answer using radicals as needed The value of d y 2 T at t is 4 at this F

Provide your answer below 6 Reflection 5 4 3 2 1 0 electing the correct reflection then move the vertical asymptote and the key point f x log4 x 3 1 2 3 4 5

Which of the following answer choices correctly gives the values of sin A cos A and tan A for the triangle shown below Select the correct answer below sin A 12cos A 2 tan A 1 2 sin A 2 cos A 2 tan A 12 12 B

The circle below has center o and its radius is 6 cm Given that mAOB 30 find the length of the major arc ACB Give an exact answer in terms of and be sure to include the correct unit in your answer 30 B A Length of major arc ACB 010 cm cm cm X

Describe everything you can say about how the following equation has been transformed from its parent function of x f x 2 x 1 5

State two different trig equations for the following graph 2 f x 3 24 X 3T T TT 0 1 2 2 M 2 3 4 5 N a

8 Given sece O a in quandrant IV find tan 0 17 O b 8 17 9 OC 17 17 Od 9

Consider the equation 2x 11x 7x 6 A student performed synthetic division on this polynomial and their work is shown below 6 11 7 12 6 6 2 1 1 0 Based on their work which is correct write the equation of the polynomial in factored form 6 2

Us eproperties of logatithms to expand the logarithmic expression as much as possible m n k 1085 1 b 3 7 a 1 Oa log m log n 210g k Oblog m log n log 4 Oc log m log m 2log 4 3 O d 3log m 7log n 2log

State the different methods one can use to solve a system of equations Then explain which method you prefer and

Write the form of the partial fraction decomposition of the rational expression It is not necessary to solve for the constants 4x 3 x 9x 20 O a A x 4 B x 5 C x 9x 20 O b A x 4 B x 5 Cx D x29x 20 OC A x 4 B x 5 C x 4 x 5 O d A x 4 B x 5

Consider the function x2 8x 7 Which of the following is correct O vertex 4 9 intercepts 7 0 1 0 0 7 O vertex 4 9 intercepts 7 0 1 0 0 7 O vertex 4 9 intercepts 7 0 1 0 0 7 O vertex 4 9 intercepts 7 0 1 0 0 7

Match the graph with the appropriate function H 2 2 2 y f x x 2x 1 Of x x 2x 1 Of x x 2x 2 Of x x 2x 2 2 X

If a polynomial has a degree of 6 then the number of turns could be 3 O True False

14 Find the area of the shaded region on the right 16 0 y 4x y 48 16x 3 X

Find equations of all lines having slope 3 that are tangent to the curve y 3 x 9 Select the correct choice below and fill in the answer box es within your choice OA There is only one line tangent to the curve with a slope of 3 and its equation Type an equation OB There are two lines tangent to the curve with a slope of 3 The equation of the line with the larger y intercept is Type equations