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Suppose f is a differentiable function, such that (1) f(x+y)=f(x)+f(y)+2xy for all real numbers x and y and (2) lim_h-->0 f(h)/h =7.
Determine whether the statement is true or false. If it is true, explain why it is true. If false, give an example to show it is false.
Find the distance between two lookout stations and fire.lookout station a is 15 km west of station b. the bearing from a to a fire directly
The demand function for a certain make of ink jet cartridge is p= -0.01x^2 - 0.1x + 6
The data in the table below define y as a function of x.
Using the appropriate substitution method and the quotient rule find the integral of:
Trigonometry Word Problems.A surveyor is measuring the distance across a small lake. He has set up his transit on one side of the lake 130 feet from a piling
The derivative of a continuous function at x is the slope of the tangent line to the curve at x. The attached pdf file develops the idea of a derivative
Completing Trigonometric Identities. Complete the Identity:
Trigonometry : Graphs, Asymptotes and Phase Shifts.If sin(alpha)=1/5 where alpha is in quadrant II, find the remaining five trigonometric functions of alpha
A formula is derived for the n-th derivative of a function that is a product of two other functions, f(x)=u(x).v(x)
Trigonometric Identities for Secant and Tangent. Match sec4 y - tan4 y to one of the following:
Assume F has characteristic 0 and K is a splitting field of f (x) in F[x]. If d(x) is the greatest common divisor of f(x) and f ' (x) and h(x) = f(x) / d(x)
Trigonometric Functions. Which one of the following trigonometric functions of x is not correct?
Trigonometry and Heart Rates.Digging up the street. A contractor wants to install a pipeline connecting point A with point C on opposite sides of a road.
Using rectangles whose height is given by the value of the function at the midpoint of the rectangles base (the midpoint rule); estimate the area
When the means is 70 and the standard deviation is 15 what is the percentage of rates less than 70, what is the relative frequency of rates less than 40
Find the derivatives of the following functions, and simplify into the forms specified. (a) g(x)=x^(12) (9 ln x + 15)
Trigonometry Word Problem - Football Game Suppose at kickoff of a football game, the receiver catches the football at the left side of the goal line and runs
Latitude and Nautical Mile.A nautical mile depends on latitude. It is defined as length of a minute of arc of the earth's radius
Let f(x)={(x^3)cos(1/x) if xâ? 0, 0 if x=0, and g(x)={(1/x)sin(x) if xâ? 0, 0 if x=0.
You are in the market for oranges. The supply equation (in millions) for oranges is : S(P)= .3p^2 +11P - 40
Determine the values of x, if any, at which the function is discontinuous. At each number where f is discontinuous, state the condition(s) for continuity
Derivatives : Trigonometry Rate of Change Problems.A fugitive is running along a wall at 4.0m/s. A searchlight 20m from the wall is trained on him.
Trigonometry and conic sections.Give a polar equation for the curve whose graph is a vertical line that passes 3 units to the right of the origin.