Letf be the function given by f(x)--16x2 +64x and let line l be the line tangent to the graph off...
5. Let R be the region bounded by the graph of, y Inr + 1) the line y 3, and the line x - 1. (a)Sketch and then find the area of R (b) The region R is the base of a solid. For this solid, each cross section perpendicular to the x-axis is an equilateral triangle. (c) Another solid whose base is also the region R. For this solid, each cross section perpendicular to the x-axis is a Semi-circle...
Let f be the function defined by F(x)=(1/2)(x+2)^2 for [-2,0) and 2-2sin(sqrtx) for [0, (x^3)/4]. the graph of f is shown in the figure above. Let R be the regiok bounded by the graph of f and the x-axis. for -25=co for osca Let I be the function defined by 1 (2) - {}(2+2) (2-2n The graph of fis shown in the figure above. Let R be the region bounded by the graph off and the ads (a) Find the...
4. (Calculator) Let R be the region bounded by the graphs of f(x)= 20+x-x2 and g(x)=x-5x. (a) Find the area of R. (b) A vertical line x k divides R into two regions of equal area. Write, but do not solve, an equation that could be solved to find the value of k (c) The region R is the base of a solid. For this solid, the cross sections perpendicular to the x-axis are isosceles right triangles with the hypotenuse...
1. 2. 3. The function defined by f(x) = x4 + 4x3 - 16x2 - 64x has the graph, as shown. 200- X Use the graph to factor the polynomial. 7 -200 What is the factored form of the polynomial? f(x) = (Simplify your answer. Type your answer in factored form.) Graph the polynomial function f(x) = 2x3 X° + 1. Then answer parts a and b. Choose the correct graph below. O A. OB O c. OD У AY...
1a. Find the equation y-f(x)-f'(x.)*(x-%) of a tangent line to the graph of a polynomial function f(x) -2xN4-x+3 3x^*2 at the point x, -1. (See the files Derivatives.doc and Derivatives of a power function.doc) N-16 1 b. Find the equation y-f(xi)-f'(x.)*(x-%) tangent line to the graph of a function of a f(x)-4x atx, 2. (Use the chain rule of differentiation for finding f'(x,).)
Find the equation of the line tangent to the graph of f(x) (In x) atx = 5 (Type your answer in slope-intercept form. Do not round until the final answer. Then round to two decimal places as needed.)
DO ALL PARTS PLEASE Let f and g be the functions defined by f(x) = 1 +x+7-24 and g(x) = x* -6.572 +6x + 2. Let R and S be the two regions enclosed by the graphs off and g shown in the figure above. (a) Find the sum of the areas of regions R and S. (b) Region S is the line of a solid whose cross sections perpendicular to the x-axis are squares. Find the volume of the...
Find the derivative of the function. f(x) = arccsc 8x -1 f'(x) = x\V 16x2 – 1 10 ny Find an equation of the tangent line to the graph of the function at the given point. y = - arccos y 37 2 xt. = - arccOS X
cannot figure out how to write the integrals for this problem #2 1. If glx) -2x and fx) - , find the area of the region enclosed by the two graphs. Show a work for full credit. (4 pts) 2. A:12-80% 3 3 2 Let fix)-. Let R be the region in the first quadrant bounded by the gruph of y - f(x) and the vertical line x # l, as shown in the figure above. (a) Write but do...
Let R be the region in the first quadrant bounded by the x-axis and the graphs of y = in(x) and y=5-x, as shown in the figure above. a) Find the area of R. b) Region R is the base of a solid. For the solid, each cross-section perpendicular to the x-axis is a right isosceles triangle whose leg falls in the region. Write, but do not evaluate, an expression involving one or more integrals that gives the volume of the solid. c)...