Find the maximum area of a triangle formed in the first quadrant by the x-axis, y-axis, and a tangent line to the graph of y = (x+1)^-2
Find the area of the smallest triangle formed by the x axis, y axis, and a line that goes through the point (4,2). Type an integer or a number with two decimal points. Area :
6. (20 points) Find the centroid of the region in the first quadrant bounded by the z-axis. 1-y2, and the line x + y 2. 6. (20 points) Find the centroid of the region in the first quadrant bounded by the z-axis. 1-y2, and the line x + y 2.
Let f(x) k sin(kx), where k is a positive constant (a) Find the area of the region bounded by one arch of the graph f and the x -axis. b) Find the area of the triangle formed by the x -axis and the tangents to one arch nts to one arch of f at the points where the graph of f crosses the x -axis Let f(x) k sin(kx), where k is a positive constant (a) Find the area of...
Math232 2 Consider the region in first quadrant area bounded by y x,x=6, and the x-axis. Revolve this bounded region about the x-axis a) Sketch this region and find the volume of the solid of revolution; use the disk method, and show an element of the volume. (15 marks) b) Find the coordinates of the centroid of the solid of revolution Find the moment of inertia of the solid of revolution with respect to the x-axis. d) Math232 2 Consider...
Find the equation of the tangent line to the graph y=x√ at x=4. y = On graph paper, sketch the graph and the tangent line using the x-values 3.5,4,4.5. The tangent line provides a linear approximation to x√ near x=4. Use this approximation to find approximate values for 4.5‾‾‾√ and 5√
The tangent line to the graph of f(x) at x 1 is shown. On the tangent line, P is the point of tangency and A is another point on the line. A y f(x) X -2 2 3 -2 -3 (a) Find the coordinates of the points P and A P(x, y) A(x, y) (b) Use the coordinates of P and A to find the slope of the tangent line (c) Find f'(1) (d) Find the instantaneous rate of change...
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)...
2. Use Definition to find the equation of the tangent line to the graph of the equation y- 1/2 at -2 3. Find the points on the graph of y2-/2 at which the tangent line is parallel to the line y - 3. 4. Sketch the graph of a continuous function f that satisfies all of the stated conditions. f(0) 2, f(-2)- (2)-0, f(-2) f(O)-f'(2)-0 f"(z) > o if-2<zco, f,(z) < 0 if <-2 or x > 0; 2. Use...
Find the maximum possible area of a rectangle in quadrant 1 under the curve y = (x − 6)^2. (Include a test showing that your rectangle’s area is the maximum possible.)
Math23 2 Consider the region in first quadrant area bounded by y x, x 6, and the x-axis. Revolve this bounded region about the x-axis a) Sketch this region and find the volume of the solid of revolution; use the disk method and show an element of the volume. (15 marks) b) Find the coordinates of the centroid of the solid of revolution. c) Find the coordinates of the centroid of the plate; on the sketch above, show the vertical...