Calculus question and answers for December 20, 2023
- Q Question 5 Find an equation of the circle that has center 5 1 and passes through 1 5 0
- Q Rewrite cos tan w as an algebraic expression in w cos tan w S
- Q Greg and Charmaine are standing on a riverbank 100 meters apart at points A and B respectively See the figure below They want to know the distance from Charmaine to...
- Q Use logarithmic differentiation to find dy dx y x x 44 x 0 dy dx 11
- Q Consider the following y 7x In x 1 7 Find an equation of the tangent line to the graph of the function at the given point Use a graphing utility...
- Q Given r x a f x dx 10 and b f c f x dx d f x dx f x dx S af rex 3f x dx f x...
- Q Use sigma notation to write the sum 5 4 2 4 1 4 3 5 4 14
- Q Use the Second Fundamental Theorem of Calculus to find F x X 1 E 3 dt 4 7 F x F x
- Q Evaluate the definite integral 649 e 36 Submit Answer dx xv In x
- Q Evaluate the definite integral x 1 2x 4 dx
- Q Evaluate the indefinite integral 1 COS X 18 sin 8 x dx
- Q Evaluate the indefinite integral e7x 12042 e7x 2 dx C
- Q Evaluate the indefinite integral 1 sec 30 tan 30 de C
- Q Since u 2 3x then converting back to an expression in x we get the following Remember to use absolute values where appropriate Inl Injul C
- Q Now if u 2 3x then dx xx du 1 du 2 3x This evaluates as the following Remember to use absolute values where appropriate 11 du
- Q Since u 8 x then converting back to an expression in x we get 1 c 28 C
- Q Step 1 We must decide what to choose for u If u f x then du f x dx and so it is helpful to look for some expression in...
- Q Now if u 8 x4 then This evaluates as x s dx us du 1 us du 8 x4 6 dx
- Q x 18 We must also convert x dx into an expression involving u If u 8 x is substituted into x 8 x4 6 dx then we have We know...
- Q Evaluate the integral by making the given substitution x 8 x 6 dx u 8 x x4 6 Part 1 of 4 We know that if u f x then...
- Q Determine the convergence or divergence of the series If you need to use co or 00 enter INFINITY or INFINITY respectively n 1 4n 1 lim no 3n 1 converges...
- Q Evaluate the integr l by making the given substitution Je 4x 4x dx U 4x
- Q Find the average value of f x 2 Vx 1 X 1 x 6
- Q Find the average value of f x x 1 15 x 6 s X
- Q The linear density p in a rod 7 m long is 12 X 9 Pave kg m where x is measured in meters from one end of the rod Find...
- Q Evaluate the integral using the indicated trigonometric substitution Use C for the constant of integration 4x 25 O CHOICE C Sketch and label the associated right triangle CHOICE A X...
- Q Evaluate the integral 0 6 x2 9 25x2 dx
- Q Find the average value of f on 0 16 1 0 4 100 8 12 AX
- Q Consider the following function x x 3 a Determine an appropriate trigonometric substitution O Use x 3 sin 0 where 1505 12 24 0 since the integrand contains the expression...
- Q Consider the following function x6 dx 1 x a Determine an appropriate trigonometric substitution Use x Use x sin 8 where tan 8 where T T 0 since the integrand...
- Q sin x Since cos x is the derivative of sin x then 12 sin x cos x dx can be done by substituting u Step 4 With the substitution u...
- Q The series True O False 00 n 0 n 2 1 converges
- Q lim 0 converges O diverges convergence or divergence of the series If you need to use coor co enter INFINITY or INFINITY respectively
- Q Evaluate the integral 4 0 sin5 x dx
- Q Tutorial Exercise Evaluate the integral 1 Step 1 12 sin x cos x dx Since S 12 sin x cos x dx has an odd power of of cos x...
- Q 1 Determine function f x x Power series for the
- Q converges conditionally converges absolutely diverges Need Help Submit Answer nwi Read It 6 25 6 25 Points Determine whether the series converges absolutely or conditionally or diverges COS n Watch...
- Q Find the average value of f on 0 16 y 1 0 t 8 12 4X
- Q An alternating series always converges True False
- Q College students were given three choices of pizza toppings and asked to choose one favorite The following table shows the results Find the probability that the favorite topping is meat...
- Q How many four digit passcodes are possible if the first digit can not be five and repetition is not allowed Write the answer as a whole number
- Q In a statistics class there are 23 juniors and 19 seniors 9 of the seniors are females and 15 of the juniors are males A student is selected at random...
- Q Two dice are rolled one time Find the probability of getting a sum of 6 or doubles O 10 36 11 36 O 12 36 9 36 13 36
- Q A couple has three children Find the probability of getting two boys 18 48 0 3 8 05 8
- Q Two coins are tossed one time Find the probability of getting one head O 2 1 8 4
- Q Two cards are drawn with replacement from a deck of cards Find the probability of selecting a king and a face card in order 0 083 O 0 143 0...
- Q Problem 54 Find the intervals on which f x is increasing the intervals on which f x is de creasing Then sketch the graph Add horizontal tangent lines f x...
- Q Two marbles are drawn without replacement from a box with 4 blue 3 white and 2 red marbles Find the probability of selecting a blue and a red marble in...
- Q In a certain college 33 of the physics majors belong to ethnic minorities Find the probability of the event from a random sample of 7 students who are physics majors...
- Q Find the exact length of the curve y 2 3 1 4 2 3 10 3 1 x 2 0 x 5
- Q A student takes a multiple choice test of 10 questions with four choices and guesses on each question Find the probability that the student gets exactly 7 correct answers 0...
- Q There are 10 members on a board of directors If they must elect a chairperson a secretary and a treasurer how many different slates of candidates are possible Write the...
- Q A symphony decides to raise money by raffling off an oven worth 500 a dinner worth 170 and a set of books worth 125 A total of 2000 tickets are...
- Q A bag contains 5 cherry 2 orange and 3 lemon candies You reach in and take 3 pieces of candy at random Find the probability of selecting 1 orange and...
- Q There are 8 women and 6 men in a department A committee of six people is to be selected How many different ways can the committee be selected if there...
- Q A shirt company has 5 designs each of which can be made with short or long sleeves There are 8 color patterns available How many different types of shirts are...
- Q Find the simple interest on the loan Round your answer to the nearest dollar 6750 at 4 5 for 8 months
- Q Find the future value of the loan Round the answer to the nearest dollar 9570 at 4 35 for 8 years
- Q Maximize Subject to Maximum is X y z 4x 3y 3x 7y 5x 3y X Y 56 50 0 0
- Q Find the absolute minimum and absolute maximum values of f on the given interval 281 81 81 Step 1 The absolute maximum and minimum values occur either at a critical...
- Q Consider the following graph y 5 4 3 2 1 1 2 3 4 5 6 X a Find the interval s on which f is increasing Enter your answer...
- Q F x x4 5 x 9 X Enter your answers as a comma separated list If an answer does not exist enter DNE Enhanced Feedback To find critical numbers of...
- Q Use the graph of the derivative f of a continuous function f is shown Assume f continues to co y 4 X 2 2 X 2 y f x a...
- Q Problem 66 Summarize the pertinent information obtained by applying the graphing strategy and sketch the graph of f x 3x5 5x Domain Range Increasing Decreasing interval s Concavity or concavities...
- Q Find the critical numbers of the function Enter your answers as a comma separated list If an answer does not exist enter DNE 1 2 2 f x 9 1...
- Q C Problem 70 Summarize the pertinent information as in previous problem obtained by applying the graphing strategy and sketch the graph of f x 2e0 5x e 0 5x
- Q Problem 28 Use L Hopital s rule to find the limit 3x lim x0 ex 1
- Q 4 T shirt manufacturer is planning to expand its workforce It estimates that the number of T shirts produced by hiring x new workers is given by T x 0...
- Q C Problem 36 Find the intervals on which the graph of F is concave upward the interv which the graph of f is concave downward and the x y coordinates...
- Q Problem 38 Determine the limit lim x 0 3x 1 e3x x
- Q Problem 46 Find the intervals on which f x is increasing the intervals on which f x is de creasing and the local extrema f x x 2 e
- Q Consider the following 9 6 3 Let t 9 tan 0 and determine the following a dt t 0 0 dt 81 2 t 9 0 Evaluate the integral de
- Q Section 11 3 L Hopital s Rule Problem 26 Use L Hopital s rule to find the limit x 1 x1 ln x3 lim
- Q x 1 Step 1 Recall the Inverse Substitution Rule where f and g are differentiable functions and g is one to one R x dx We are given the following...
- Q Find the average value of f x IN 2 X 1 x 3
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