Questions from General Calculus

Q: Explain, in terms of linear approximations or differentials, why the

Explain, in terms of linear approximations or differentials, why the approximation is reasonable. ln 1.05 ≈ 0.05

Q: If, in Example 4, one molecule of the product C

If, in Example 4, one molecule of the product C is formed from one molecule of the reactant A and one molecule of the reactant B, and the initial concentrations of A and B have a common value [A]= [B]...

Q: Find the differential of each function. (a). u

Find the differential of each function. (a). u + 1/u - 1 (b). y = (1 + r3)-2

Q: Find the differential of each function. (a). y

Find the differential of each function. (a). y = etan πt (b). y = √1 + ln z

Q: Let y = ex/10. (a). Find

Let y = ex/10. (a). Find the differential dy. (b). Evaluate dy and ∆y if x = 0 and dx = 0.1.

Q: Let y = √x. (a). Find the

Let y = √x. (a). Find the differential dy. (b). Evaluate dy and ∆y if x= 1 and dx = ∆x = 1. (c). Sketch a diagram like Figure 6 showing the line s...

Q: Find an equation of the tangent line to the curve at the

Find an equation of the tangent line to the curve at the given point. y = ln (xex2), (1, 1)

Q: The radius of a circular disk is given as 24 cm with

The radius of a circular disk is given as 24 cm with a maximum error in measurement of 0.2 cm. (a). Use differentials to estimate the maximum error in the calculated area of the disk. (b). What is the...

Q: The circumference of a sphere was measured to be 84 cm with

The circumference of a sphere was measured to be 84 cm with a possible error of 0.5 cm. (a). Use differentials to estimate the maximum error in the calculated surface area. What is the relative error?...

Q: Sketch the parabolas y = x2 and y = x2 – 2x

Sketch the parabolas y = x2 and y = x2 – 2x + 2. Do you think there is a line that is tangent to both curves? If so, find its equation. If not, why not?