Calculus question and answers for January 16, 2024
- Q Determine the global extreme values of the function on the given set without using calculus f x y 2e 2 8y z 8y 1 fmin
- Q The function f has continuous second derivatives and a critical point at 10 1 Suppose faz 10 1 2 f 10 1 1 f 10 1 4 Then the point...
- Q Calculate the directional derivative of f z y sin y in the direction of v 1 23 at the point P 0 5 0 5 Remember to normalize the direction...
- Q Consider the function f x y cos 9y Find and classify all critical points of the function If there are more blanks than critical points leave the remaining entries blank...
- Q Find the equation of the circle shown in the figure LAHA 3 2 1 y 3 1 1 2 X
- Q Make a table of values and sketch the graph of the equation Find the x and y intercepts and a x 3y 6 Make a table of values and sketch...
- Q Find the critical points of the function f x y x y 144xy Answer 8 Starting with the point with the smallest z value use the Second Derivative Test to...
- Q Find the x and y intercepts of the graph of the equation If an answer does not exist enter DNE 9x 4y 36 x intercept x intercept x y y...
- Q Let f x y x y and c t t 2t a Calculate Vf c t B b Use the Chain Rule for Paths to evaluate f c t at...
- Q Calculate the gradient of h x y z x 2 Vh
- Q Find the gradient of the function f x y z xy at the point 1 1 0 Vf 1 1 0
- Q Make a table of values 4x 5y 45 No Solution X Help 3 2 1 0 1 2 3 Sketch the graph of the equation y 15 1413 12 11...
- Q Find an equation of the circle that satisfies the given conditions Center at the origin passes through 5 8
- Q Instructions Use algebraic techniques to solve problems unless otherwise instructed Show the calcula to your answers except basic arithmetic when there is work to show Simplify and circle your final...
- Q A spherical balloon with radius r inches has volume V r r Find a function that represents the amount of air required to inflate the balloon from a radius of...
- Q The position of a particle moving on a horizontal line where s is in feet to the right of a fixed reference point and t is in seconds after the...
- Q f x The graphs of f x and g z are given above Use them to evaluate each quantity below Write DNE if the limit or value does not exist...
- Q 1 Graph on graph paper or coordinate plane lined paper will not earn credit List the domain and range in interval nota a f x b f x x 51...
- Q 3 Jasin if x 0 z sin if x 0 Determine whether or not f 0 exists Let f 1 Answer Yes or No
- Q Let f x 5 x 4 6 Then f x 35x 40 x 30 2 x f 3 261 45
- Q If a ball is thrown vertically upward from the roof of 32 foot building with a velocity of 48 ft sec its height after t seconds is s t 32...
- Q If f x 0 10z sin determine whether or not f 0 exists 0 Answer Yes or No 2 if x if x
- Q The limit f x lim hs0 0 2 h h is the standard expression defining the derivative of some function f x at some number a Find and a 4
- Q Let h x 7 2x Use this to find the equation of the tangent line to the curve y 7 2 at the point 1 5 and write your answer...
- Q Find an equation of the tangent line to the curve y 5 2x 3x at 1 0 V
- Q The limit 81 h 9 h lim h 0 is the standard expression defining the derivative of some function f x at some number a Find f and a f...
- Q 2 Write a piece wise function for each graph a MAY b 10
- Q For the following exercises find the domain of each function expressing answers using Interval notation 3 4 5 2 3x 2 x 3 f x 4x 12 x 4
- Q 3 10 pts Calculate the difference quotient of f x 7x 5x 9
- Q 2 12 pts For f x x 3 a calculate f 5x and 5f x and b f x 2 and f x f 2
- Q Labie gives the number w Q d t 2000 2002 2004 t 2006 2008 2010 2012 2014 N t thousands 2000 306 5 2002 900 2004 497 5 2006 899...
- Q Consider the following matrix A and it s inverse A 1 2 1 1 2 1 2 By hand calculate the condition number of A using the infinity norm 1...
- Q lies on the curve y sin 147 a If Q is the point x sin 147 find the slope of the secant line PQ correct to four decimal places for...
- Q Find the limit 19 lim 8 X 8 1 x2 A x2 7x 3 x x3 6x2 4 20 lim A 00 B 8 B 314 C 1 C 1...
- Q 2 The graph of a function f x is given below It consists of three line segments for 0 x 8 Each mark along the x axis and y axis...
- Q 3 0 25 0 31 Points DETAILS 1 1 2 4 A graphing calculator is recommended The displacement in centimeters of a particle s moving back and forth along a...
- Q x2 7x 3 X 00 x3 6x2 4 20 lim A DO B 314 C 1 D 0
- Q Calculate the derivative of the function by using the formula f x Lim h 0 26 g x 3x2 4x A g x 6x 27 f x 8 X 8...
- Q rovide an appropriate response 22 Use the Intermediate Value Theorem to prove that 8x4 4x3 7x 5 0 has a solution between 1 and 0 22
- Q In 2003 the first complete human genome was sequenced Based on data from the National Human Genome Research Institute 4 the cost of sequencing a human genome in January 2004...
- Q a b C Find z if a 2 log 4 log 5 log 10 log b log 30 log 52 log c log 8 log a log a d log...
- Q d log 5 e log3 y 5 f log 4x 5 d e if y X log then X by
- Q 2 Write the equation of the following line in 4x 3y 8 a Slope intercept form b Point slope form
- Q Find a function whose graph is a parabola with vertex 1 5 and that passes through the point 5 11
- Q Example 1 Find an equation of the tangent line to the function y at the point P 1 4 Solution We will be able to find an equation of the...
- Q The point P 4 4 lies on the curve y a If Q is the point 1 3 9 mpqQ ii 3 99 mpQ iii 3 999 mpQ iv 3...
- Q Rewrite using only positive rational exponents 5 45 2 54 6a b
- Q Rewrite using only positive rational exponents 5x 3yz 4 3 5x 3yz Type a single expression raised to a positive expon
- Q Use the laws of exponents to simplify 3 4 3 3 3 8 3 3 8 3 Simplify your answer Type exponential notation with posit
- Q Rewrite with rational exponents 5 3 xy z 5 xy Sim
- Q Rewrite with positive exponents 7x 1 8 1 7x Type exponential notation with positive exponents Use integers any numbers in the expression
- Q Rewrite without rational exponents and simplify if possible 1 6 Simplify your answer Type an exact answer using radicals as nee
- Q Rewrite with rational exponents 9 S
- Q Rewrite 64 64 1 with a positive exponent then simplify
- Q Rewrite with rational exponents 5 13 9x6y
- Q Rewrite with rational exponents 5 xy z 3
- Q 49 The solution is Simplify your answer Type an integer or a fraction
- Q 6 Apply the Intermediate Value Theorem to determine on which of these intervals the graph of f x 2x 7x 1 must intersect the line y 4 A 8 6...
- Q A ball is thrown into the air by a baby alien on a planet in the system of Alpha Centauri with a velocity of 46 ft s Its height in...
- Q Population Growth The graph of P t below shows the population in thousands of people of a city t years after 2008 Note that 8 years after 2008 the population...
- Q Use the graph of f to evaluate the following 6 5 1 4 3 Next question 2 1 14 Get a similar question 8 1 2 3 4 5 6...
- Q Given f x 1 find the average rate of change of f x on the interval 5 5 h Your answer will x 8 be an expression involving h
- Q 10 81 4 2 6 4 1 2 2 4 2 A 4 6 8 10 12 6 Clear All Draw Dot Line Segment a Mark the two points on...
- Q Use the graph of f to evaluate the following 1 6 5 4 3 2 1 1 f x 2 3 4 5 X of The average rate of change...
- Q Given f x x 7 find an expression that gives the slope of the line from 2 2 to 2 h f 2 h Your answer will be an expression...
- Q Let x 2 2 A Sketch the graph of f and when you re done place a 1 in the box values B Find the value of a where f...
- Q A spherical balloon is being inflated Find the rate of increase with respect to its radius in inches r of the surface area in square inches S 4T when A...
- Q At what point does the line normal to the graph of y 3x 3 4x at 1 4 intersect the parabola a second time 0 Hint The normal line is...
- Q 2 Write the equation of a line that is perpendicular to y 8 x 1 and passes through 4 1
- Q Find equations of the tangent line and of the normal line to the curve y 5 2x 2 at the point 1 49 Write the equations of the lines in...
- Q For what value s of a is the tangent line to the graph of parallel to the line y 2x 0 4 f x 4x 6x 142x 48 If there...
- Q Let f x 8 Then the expression f x h f x h where A is a constant and A I Using your answer from above we have f x...
- Q Let f x x 8 Evaluate the following limits T lim Z 8 lim f x f 8 x 8 CAMENTE f x 8 x 8 Thus the function 2...
- Q Find the equation of the tangent line to the curve y 6 sin x at the point 6 3 z The equation of this tangent line can be written in...
- Q Find the points on the graph of f x 2x 2x 3 List the x values of these points I value s Separate answers by commas if ther 6x 6x...
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