Calculus question and answers for October 19, 2023
- Q A cylindrical can has a volume of 1458? cm. What dimensions yield the minimum surface area?The radius of the can with the minimum surface area is cm.(Simplify your answer.)The height...
- Q Find the degree, leading term, leading coefficient, and the maximum number of real zeros of the given polynomial.f(x) = -x- 5x? - 3x? +6Degree: 7, the leading term: 3x7, the...
- Q Find the points on the cone z = x + y that are closest to the point (8, 2, 0).smaller z-value (x, y, z) =larger z-value (x, y, z) =
- Q Each side of a square is increasing at a rate of 7 cm/s. At what rate (in cm/s) is the area of the square increasing when the area of the...
- Q Find the derivative of the function.f(x)=2x?-6e12x? - 12e12x?12x? - 12e12x? - 6e
- Q Find the derivative of the function.y = (3x+1)?(x? ? 6)?y' = (24x + 12) (3x + 1)?(x? - 6)?y' = 12(3x + 1) (x? - 6)? +24x (3x + 1)?...
- Q Find the derivative of the function.g(t)=tan(cos 2t)sin 2t sec(cos 2t)2sin 2t sec(cos 2t)-sin 2t sec(cos 2t)-2sin 2t sec (cos 2t)
- Q Find an equation of the line tangent to f(x)=x^2-4x at the point (3, -3).x-2y=9y-2x = 92y-x=92x - y = 9
- Q 2(x - 5) + (y-4) + (z-7^)2 = 10, (6, 6, 9)(a) Find an equation of the tangent plane to the given surface at the specified point.(b) Find an equation...
- Q Find f'(x).f(x) = (6x + 9)(8x - 3)f'(x) =(Type an exact answer.)
- Q Find f'(x) and simplify.f(x) = x / x +39Which of the following shows the correct application of the quotient rule?A.(x +39)(1)-(x)(1)/[x+39]B. (x +39)(1)-(x)(1)/[x]C.(x)(1)-(x +39)(1)/[x+39]D. (x)(1)-(x +39)(1)/[x]f'(x) =
- Q Replace ? with an expression that will make the equation valid.d/dx (7x+2)? = 9(7x+2)? ?The missing expression is
- Q Assume that x = x(t) and y = y(t). Let y = x +1 and dx/dt = 3 when x = 1.Find dy/dt when x = 1.dy/dt = (Simplify your...
- Q Use implicit differentiation to find y' for the equation below and then evaluate y' at the indicated point.y+3y + 2x=0; (-2,1)y' = y'l(-2,1) = (Simplify your answer.)
- Q When asked to simplify the following expressions, a student came up with the following plans. Unfortunately, they are incorrect. Point out what is wrong and give correct answers.a) Simplify x/x+4...
- Q Find the relative rate of change of f(x) = 10 + 2e^-2xThe relative rate of change of f(x) is
- Q Find dy/dx for the indicated function y.y = 10x + e
- Q If xy = 4 and dx/dt = -5, then what is dy/dt when x = 4 and y = 1?
- Q Use the formula f'(x) = lim z?x f(z) - f(x) / (z-x) to find the derivative of the function.g(x) = x/ (x+ 9)
- Q A ball dropped from the top of a building has a height of s= 256 - 16t meters after t seconds. How long does it take the ball to reach...
- Q Find the derivative of f(x)=x using limits
- Q A certain function f has inverse function f?(x) = x + 2x + 1. Use this to solve for x in theequation 3f(x) - 1 = 5.(Hint: First solve for...
- Q Suppose f'(x) is continuous over an interval ? ? x ? b, and a < c < d < b.If f'(c) = 5, then (check all that apply)f(x) is decreasing...
- Q Use the chain or general power rules to determine the derivative of the following function.f(x)=(5-6x+2x)
- Q Let a?0 be a complex number, and define the ?th branch of z by f(z) := exp(aLog?(z)). Show that, for z C R?, we have '(z) = af(z)/z. This means...
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