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- Differentiate the functions showing the general process in determining the derivatives. Using the delta y and x and applying limits .How is derivatives utilized in solving for the dimensions and total area of a box?Find the coordinates of the point (x,y) on the curve y=2x+1 that is closest to the point (6,3) .{ Hint: find the minimum of the square of the distance) . use a derivative test to verify that your answer is optimal
- Does this fuction have a minimum value?Suppose you find the linear approximation to a differentiablefunction at a local maximum of that function. Describe the graphof the linear approximation.How do I solve the derivative for x to find the critical points and identify the absolute minimum and maximum?
- Find the dimensions of a cylinder (i.e. the radius of the base and height) without a top that has a volume of 4000 cubic centimeters and has the least amount of surface area. Use the first or second derivative test to establish that the dimensions you found do indeed yield the minimum surface area.All edges of a cube are expanding at a rate of 6 centimeters per second. How fast is the surfacearea changing when each edge is 2 centimeters? Use the limit definition of a derivative to find f'(x) if f(x)= 1/(x-2). Find the equation of the tangent line to the graph of x + y - 1 = In(x^2 + y^2) at the point (1, 0).Pls use limit no differential and could you please do the solution on paper because i am not good at englısh thx :)
- Given a right circular cone with an altitude of 5 cm and a base diameter of 8 cm. If the diameter is increased by 0.04 cm and the altitude is likewise increased by 0.03 cm, find the approximate increase in volume. Use partial derivative for your detailed solution.how do limits relate to derivatives and integrals? also give examples of when they are used to slove real life problemsFind the slope of the tangent line to the curve y=1+1x at x =2. Do not use the derivative but rather the slope of the secant line through the points (2,f(2)) and (2+h,f(2+h)), then take the limit as h→0. Sketch the graph of the curve, the secant line, and the tangent line on the same coordinate system.