Question

In: Math

1)For the function f(x)=6x^2−2x, evaluate and simplify. f(x+h)−f(x)/h 2)Evaluate the limit: limx→−6 if x^2+5x−6/x+6 3)A bacteria...

1)For the function f(x)=6x^2−2x, evaluate and simplify.

f(x+h)−f(x)/h

2)Evaluate the limit: limx→−6 if x^2+5x−6/x+6

3)A bacteria culture starts with 820820 bacteria and grows at a rate proportional to its size. After 22 hours there will be 16401640 bacteria.

(a) Express the population PP after tt hours as a function of tt. Be sure to keep at least 4 significant figures on the growth rate.
P(t)P(t)=

(b) What will be the population after 8 hours?
bacteria

(c) How long will it take for the population to reach 2450? Give your answer accurate to at least 2 decimal places.
hours

Solutions

Expert Solution


Related Solutions

2. Let f(x)=2x^2−4x+7/5x^2+5x−9, evaluate f '(x) at x=3 rounded to 2 decimal places. f '(3)= 3....
2. Let f(x)=2x^2−4x+7/5x^2+5x−9, evaluate f '(x) at x=3 rounded to 2 decimal places. f '(3)= 3. Let f(x)=(x^3+4x+2)(160−5x) find f ′(x). f '(x)= 4. Find the derivative of the function f(x)=√x−5/x^4 f '(x)= 5. Find the derivative of the function f(x)=2x−5/3x−3 f '(x)= 6. Find the derivative of the function g(x)=(x^4−5x^2+5x+4)(x^3−4x^2−1). You do not have to simplify your answer. g '(x)= 7. Let f(x)=(−x^2+x+3)^5 a. Find the derivative. f '(x)= b. Find f '(3)= 8. Let f(x)=(x^2−x+4)^3 a. Find the...
For the function f(x) = x^2 +3x / 2x^2 + 6x +3 find the following, and...
For the function f(x) = x^2 +3x / 2x^2 + 6x +3 find the following, and use it to graph the function. Find: a)(2pts) Domain b)(2pts) Intercepts c)(2pts) Symmetry d) (2pts) Asymptotes e)(4pts) Intervals of Increase or decrease f) (2pts) Local maximum and local minimum values g)(4pts) Concavity and Points of inflection and h)(2pts) Sketch the curve
Suppose f(x)= 2x^3- 6x^2 + 1 For what x is f(x) increasing? decreasing? What are the...
Suppose f(x)= 2x^3- 6x^2 + 1 For what x is f(x) increasing? decreasing? What are the local minimum and maximum values of the function f (if any)?
For the function a) f(x)=x^3-9x^2+23x-15 b)f(x)=(x+3)^2(2x+1)(x-1) c)f(x)=-(x^2-6x+9)(x^2-x-6) Find: 1) the zeros 2) the y-intercept 3) left-right...
For the function a) f(x)=x^3-9x^2+23x-15 b)f(x)=(x+3)^2(2x+1)(x-1) c)f(x)=-(x^2-6x+9)(x^2-x-6) Find: 1) the zeros 2) the y-intercept 3) left-right end behavior 4) the sketch of the graph
f(x) = (2x − 3)(x 2 − 6) (a) Write formulas for f '(x) and f...
f(x) = (2x − 3)(x 2 − 6) (a) Write formulas for f '(x) and f ''(x). (b) Find all x-intercepts of f(x). (Exact answers, no decimals.) (c) Find all critical points of f(x). (x-values only; y-values not needed.) Classify them using the 1st or 2nd derivative test. (d) Find all inflection points of f(x). (x-values only; y-values not needed.)
Calc 1 Use the 11-step process to graph the function f (x)=(6x^2)/(2x^2-8)?
Calc 1 Use the 11-step process to graph the function f (x)=(6x^2)/(2x^2-8)?
1. For the function f(x)=x2−36 evaluate f(x+h). f(x+h)= 2. Let f(x)=3x+4,g(x)=9x+12, and h(x)= 9x^2+ 24x+16. evaluate...
1. For the function f(x)=x2−36 evaluate f(x+h). f(x+h)= 2. Let f(x)=3x+4,g(x)=9x+12, and h(x)= 9x^2+ 24x+16. evaluate the following: a. (fg)(3)= b. (f/g) (2)= c. (f/g) (0)= d.(fh)(-1)= 3. Let f(x)=2x-1, g(x)=x-3, and h(x) =2x^2-7x+3. write a formula for each of the following functions and then simplify a. (fh) (x)= b. (h/f) (x)= c. (h/g) (x)= 4.Let f(x)=5−x and g(x)=x^3+3 find: a. (f∘g)(0)= b.(g∘f)(0)= c. (f∘g)(x)= d. (g∘f)(x)= 5. Let f(x)=x^2+5x and g(x)=4x+5 find: a. (f∘g)(x)= b. (g∘f)(x)= c. (f∘g)(0)= d....
Evaluate the polynomial y= x^3- 5x^2+ 6x + 0.55 at x=.137. Use 3-digit arithmetic with rounding....
Evaluate the polynomial y= x^3- 5x^2+ 6x + 0.55 at x=.137. Use 3-digit arithmetic with rounding. Evaluate the percent relative error. (b) Repeat (a) but express y as y= ((x- 5)x +6)x + 0.55
Let f(x) = (x − 1)2, g(x) = e−2x, and h(x) = 1 + ln(1 − 2x). (a) Find the linearizations of f, g, and h at  a =...
Let f(x) = (x − 1)2, g(x) = e−2x, and h(x) = 1 + ln(1 − 2x). (a) Find the linearizations of f, g, and h at  a = 0. Lf (x) =    Lg(x) =    Lh(x) =  (b) Graph f, g, and h and their linear approximations. For which function is the linear approximation best? For which is it worst? Explain. The linear approximation appears to be the best for the function  ? f g h since it is closer to  ? f g h for a larger domain than it is to  - Select - f and g g and h f and h . The approximation looks worst for  ? f g h since  ? f g h moves away from L faster...
1. Find the critical numbers for the following functions (a) f(x) = 2x 3 − 6x...
1. Find the critical numbers for the following functions (a) f(x) = 2x 3 − 6x (b) f(x) = − cos(x) − 1 2 x, [0, 2π] 2. Use the first derivative test to determine any relative extrema for the given function f(x) = 2x 3 − 24x + 7
ADVERTISEMENT
ADVERTISEMENT
ADVERTISEMENT