Let f : [a, b] → R be a differentiable function and let P be a partition of [a, b]. Show that L(P, f′) ≤ f(b) − f(a). Hint: Use the Mean-Value Theorem. (Recall that, if P...

Let f : [a, b] → R be a differentiable function and let P be a partition of [a, b]. Show that L(P, f′) ≤ f(b) − f(a). Hint: Use the Mean-Value Theorem. (Recall that, if P...

If f(x)=(A+Bx)/(20+4x), with B≠0, compute f^−1(x) and f^−1(−9) in terms of A and B.

If log p=x and log q=y, evaluate the following in terms of x and y: #1) (log p^-4)/(loq q^-5) = ? #2) (log p^5)^−3 = ?

If f(x)=ln(9x+b), find f^−1(x) in terms of b.

The period T of a pendulum is the time required for a complete back-and-forth cycle. Consider a pendulum with length L, measured in meters, and period T=(3/2)(sqrtL), measured in seconds. Explain...

Define a function f by f(x)=2x−1. Find the largest number δ>0 such that, if |x−1|<δ then |f(x)−1|<12. Enter your answer as a decimal number.

Part A: If f is one-to-one and f(6)=9, then f^−1(9)= ??? and (f(6))^−1= ??? Part B: If g is one-to-one and g(7)=11, then g^−1(11) = ??? and (g(7))^−1 = ??? Not really sure...

Given g(x) = 3/(x+2), evaluate and simplify: g(5+h)-g(5) -------------- = ???? h The answer should be -3/(49+7h)...

(when 𝑎 = 0) to evaluate ln (0.4) approximately. Answer to 4 d.p. What is the exact value of ln (0.4) using the calculator (answer to 4 d.p.)?

lim x➡️-5 x+5/x^2 +7x +10

Given the electric flux density, D = 0.3 r^2 ar nC/m2 in free space: (a) find E at point P(r = 2, θ = 25◦, φ = 90◦); (b) find the total charge within the sphere r = 3; (c) find the total electric...

x^2+5*x^2-3 / x+2

= 6𝐾𝐿2 − 4𝐾 2𝐿 + 8𝐾 3where 𝐿=quantity of labour and 𝐾= quantity of capital, (a) What is the marginal productivity of labour when 𝐿 = 12 and 𝐾 = 10? (b) What is the...

I need some help with calculus homework.

2x^2-3x/x=2x-3

On a lathe, you are to turn out a disk (thin right circular cylinder) of circumference 10 inches. This is done by continually measuring the diameter as you make the disk smaller. How closely must...

If the limit definition of a derivative can be used to find f ' , then what is the purpose of using other rules to find f '

I need some help with some calculus.

Simple integration Please answer

This is a trig question my math teacher gave and i am confused. I thought the answers were 4.2 and 172.8