Calculus question and answers for January 26, 2024
- Q the following complex numbers Write the difference in star 5 9i 10i 8 9i 10i 8 Type your answer in the form a bi
- Q 8 5i 5 5i 8 5i 5 5i Simplify your answer Type your answer in the form a bi
- Q 14 14 Simplify your answer
- Q Perform the indicated multiplication 4i 2 8i 4i 2 8i Simplify your answer Type your answer in the form a ba
- Q EX 9 9 Simplify your answer Type your answer in the form a b
- Q 7 lim x 0 Hint Use the identity Vx x x 0
- Q 1 lim 2x 6 Hint Use the inequality a b a bl M x 3 which holds for all constants a and b see Exercise 74
- Q 2x 2 17 Finding a symmetric interval Let f x and note x 1 that lim f x 4 For each value of e use a graphing utility to find...
- Q 1 lim x 16 x 4 x 4 8 Hint Factor and simplify
- Q 29 lim x 3x 10 x 2
- Q 3 Finding for a given e using a graph Let f x x 3 and note that lim f x 3 For each value of e use a graphing utility...
- Q 1 Determining values of 6 from a graph The function in the fig ure satisfies lim f x 6 Determine the largest value of 8 0 x 3 satisfying each...
- Q Suppose f z is continuous on 4 7 and 4 f x 4 for all az in 4 7 Use the Mean Value Theorem to estimate f 7 f 4...
- Q Consider the function f 1 1 4z 6 on the interval 0 4 Verify that this function satisfies the three hypotheses of Rolle s Theorem on the inverval f x...
- Q Consider the function f x 5 f 7 f 4 7 4 51 on the interval 4 7 Find the average rate of change of the function on this interval...
- Q Does there exist a continuous function f x such that f 0 10 2 2 and f x 1 for all z in 0 2 Answer 2 9 ves
- Q a Evaluate the integral 32 S x 4 Your answer should be in the form k where k is an integer What is the value of k darctan a Hint...
- Q over each of the indicated intervals a Interval 10 0 1 Absolute maximum 2 Absolute minimum b Interval 7 2 1 Absolute maximum 2 Absolute minimum c Interval 10 2...
- Q The critical numbers of the function are t and t2 with tit f t 2t 3 5 3
- Q Consider the function f x 2x 9x This function has an absolute minimum value equal to and an absolute maximum value equal to 108 8 6 7 4
- Q Find all angles between 0 and 180 satisfying the given equation Round your answer to one decimal place Enter your answers as a comma separated list Enter your answer in...
- Q me function f x 7 4 e 21 has one critical number Find the critical number
- Q Use a calculator to find an approximate value in radians of the expression rounded to five decimal places if it is defined If a answer is undefined enter UNDEFINED 8...
- Q 0 1 Points 8 DETAILS sin PREVIOUS ANSWERS MY NOTES Find all angles between 0 and 180 satisfying the given equation Round your answer to one decimal place Enter your...
- Q The sun is 22 above the horizon Find the length of a shadow cast by a park statue that is 12 feet tall Round your answer to one decimal place...
- Q For what value of x is g x 1 X 16 g x
- Q After a drug is taken orally the amount of the drug in the bloodstream after t hours is f t 118 e 0 4t et units Complete the following a...
- Q Find the area of a triangle with sides of length 9 and 13 and included angle 56 48 499 32 713 86 730 Ono correct answer
- Q K A sample of 12 grams of radioactive material is placed in a vault Let P t be the amount remaining after t years and let P t satisfy the...
- Q A 680 ft rope anchors a hot air balloon as shown in the figure 680 ft 0 a Express the angle 0 as a function of the height h of...
- Q A 40 ft pole casts a shadow as shown in the figure 40 ft a Express the angle of elevation of the sun as a function of the length s...
- Q A 84 ft tree casts a shadow that is 110 ft long What is the angle of elevation of the sun Round your answer to one decimal place
- Q K A news item is spread by word of mouth to a potential audience of 6 000 people The following function models the number of people who have heard the...
- Q blem 4 When a bacteria colony reaches 150 thousand it is treated with antibiotics Due to the antibiotics the bacteria population decreases by 10 each week a Find an exponential...
- Q Determining values of 6 from a graph The function f in the fig ure satisfies lim f x 5 Determine the largest value of 8 0 x 2 satisfying each...
- Q A sample of 12 grams of radioactive material is placed in a vault Let P t be the amount remaining after t years and let P t satisfy the differential...
- Q The price of a particular crop per bushel at time t in months is approximated by f t 8 0 002t 0 02e t What is the percentage rate of...
- Q ind an equation of the tangent line to the graph of y g x at x 6 if g 6 3 and g 6 5 Enter your answer as an...
- Q 000 p 43 An electronic store can sell q 1 38 cellular phones at a price p dollars per phone The current price is 106 a Is demand elastic or...
- Q 20 Points t a t 1 t 2 t 3 V The displacement in meters of a particle moving in a straight line is given by the equation of motion...
- Q 49 60 Evaluate each limit 4x 10 49 lim x2 V 2x 51 lim X T cos x 3 cos x 2 cos x 1 53 lim 7 x 3...
- Q Find all angles 8 between 0 and 180 satisfying the given equation Round your answer to one decimal place Enter your answers as a comma separated list Enter your answer...
- Q Find the exact value of the expression sec sin 1 24 25
- Q Rewrite the expression cos sin x as as an algebraic expression in x an
- Q Find the angle in degrees rounded to one decimal 39 36
- Q Find the angle in degrees rounded to one decimal O 8 10 6
- Q Find the values of the trigonometric functions of 8 from the information given csc 0 4 8 in Quadrant I sin 8 cos 8 tan 8 sec 0 cot 0...
- Q 41 48 Functions with roots Determine the interval s on which the following functions are continuous At which finite endpoints of the intervals of continuity is f continuous from the...
- Q open interval I gives rise to the succession of derivatives 9 dX d x d X dt dt dt Now a differential equation in the function X t is therefore...
- Q Sketch a triangle that has acute angle tan 6 O Find the other five trigonometric ratios of 8 2 13 sin 8 cos 8 3 13 13 csc 8 2...
- Q An entrepreneur invests in a new play The cost includes an overhead of 31 200 plus production costs of 2100 per performance A sold out performance brings in 2750 Assume...
- Q Problem 3 Let f x 7e a What are the domain and range of f b Find any asymptotes on the graph f c Find any x or y intercepts...
- Q The angle of elevation to the top of a very tall Building is found to be 8 from the ground at a distance of 1 mi from the base of...
- Q A man is lying on the beach flying a kite He holds the end of the kite string at ground level and estimates the angle of elevation of the kite...
- Q Sketch a triangle that has acute angle 8 tan 8 O cos 8 3 12 3 3 Find the other five trigonometric ratios of 8 sin 6 3 O 3...
- Q A 21 ft ladder leans against a building so that the angle between the ground and the ladder is 66 How high does the ladder reach on the building Round...
- Q Sketch a triangle that has acute angle 8 13 csc 8 13 5 10 13 2 22 2 22 A A A A 5 10 13 13 2 22 2...
- Q Sketch a triangle that has acute angle 8 cot 8 2 O cos 6 tan 6 5 2 2 Find the other five trigonometric ratios of 8 sin 0 2...
- Q Find the side labeled x X 30 19 X
- Q The bar graph on the right shows the average cost of room and board at four year public and private colleges for four selected years from 2011 through 2017 The...
- Q Find the area of a triangle with the given description Round your answer to one decimal place a triangle with sides of length 5 and 6 and included angle 74
- Q For the data set shown by the table a Create a scatter plot for the data b Use the scatter plot to determine whether an exponential function logarithmic function or...
- Q Two tugboats that are a 125 ft apart pull a barge as shown If the length of one cable is b 208 ft and the length of the other is...
- Q Use the Law of Cosines to determine the indicated angle 0 Assume a 69 01 b 36 67 and c 42 55 Round your answer to two decimal places 0...
- Q Find the area of the triangle whose sides have the given lengths Round your answer to one decimal place a 6 b 8 C 10 A
- Q Find the indicated side x Use either the Law of Sines or the Law of Cosines as appropriate Assume LA 34 and ZC 86 Round your answer to two decimal...
- Q The differential equation 1EJ The initial conditions Remarks Xlo X dX dt dX dt An da X dr 1 W a A dt f d X to dt 1 MATHEMATICS...
- Q I Though the independent variable t of the function X t in the ODE 1 is stipulated to range in the interval I we expect the solution X t of...
- Q 0 as k MATHEMATICS This last observation is true because converging te Note that in the inequalities M K 1 10 j 1 MK Kj XI K MK n Kj...
- Q About the sequence XKEZ we have the following x 1 EBx b for each 1 to b t b MKk a X 1 1 x 1 k 1 1E10 b...
- Q Proposition 3 Let x J y J be two solutions of the initial value problem dx f t x x t x dt then x t y t for all...
- Q Proof Let Ix be arbitrary Using openness of IxJ choose 8 0 such that t 8 1 8 x 8 x 8 IXJ Of Now the function is continuous on...
- Q This shows that the solutions of the order k ODE 4 can be studied in terms of the solutions of the first order ODE 5 Note that if f of...
- Q X 1 Solution We have y t 20 1 j 4 s ds 1 Thus x 1 2 2 1 3 0 2 3 ds 2 91 2 1 3...
- Q Find the volume of the region bounded by the coordinate planes the plane x y 5 and the cylinder y 9z 2 25 2 The volume is Type an exact...
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