Question

In: Math

Consider the following. f(x) = x(x2 - 10x + 30) g(x) = x2

Consider the following. 

f(x) = x(x2 - 10x + 30) 

g(x) = x2 

(a) Use a graphing utility to graph the region bounded by the graphs of the functions.

image.png

(b) ) Find the area of the region analytically 

(c) Use the integration capabilities of the graphing utility to verify your results. 

Solutions

Expert Solution

C) Using Graphing Utility the answer would be 73.833 sq. units.


Related Solutions

Consider the following functions. g(x) =x3 − 10x h(x)=4x2 + 3x f(x)=(x3 − 10x)(4x2 + 3x)...
Consider the following functions. g(x) =x3 − 10x h(x)=4x2 + 3x f(x)=(x3 − 10x)(4x2 + 3x) Find the derivative of each function. g '(x)= h '(x)= f '(x)=
approximate the area under f(x) = 10x - x2, above the x-axis, on [1,7] with n...
approximate the area under f(x) = 10x - x2, above the x-axis, on [1,7] with n = 6 rectangles using the left and right endpoint, trapezoidal rule and midpoint methods (include summation notation and endpoint values) and then find the exact area using a definite integral (include a graph with shaded region)
f(x) = −x2 + 3x and g(x) = x − 3 Find the area of the...
f(x) = −x2 + 3x and g(x) = x − 3 Find the area of the region completely enclosed by the graphs of the given functions f and g in square units.
Consider the following functions. f(x) = x − 3, g(x) = |x + 3| Find (f...
Consider the following functions. f(x) = x − 3, g(x) = |x + 3| Find (f ∘ g)(x). Find the domain of (f ∘ g)(x). (Enter your answer using interval notation.) Find (g ∘ f)(x). Find the domain of (g ∘ f)(x). (Enter your answer using interval notation.) Find (f ∘ f)(x). Find the domain of (f ∘ f)(x). (Enter your answer using interval notation.) Find (g ∘ g)(x). Find the domain of (g ∘ g)(x). (Enter your answer using...
Let f(x) and g(x) be two generic functions. Assume limx→0(f(x)+2g(x))=2 & limx→0(f(x)−g(x))=8. Compute limx→1(f(lnx)/g(x2−x)). A. It...
Let f(x) and g(x) be two generic functions. Assume limx→0(f(x)+2g(x))=2 & limx→0(f(x)−g(x))=8. Compute limx→1(f(lnx)/g(x2−x)). A. It cannot be computed B. 2 C. 4 D. -3 E. -4
For f(x)=9x+5 and g(x)=x2 find the following composite functions and state the domain of each a)...
For f(x)=9x+5 and g(x)=x2 find the following composite functions and state the domain of each a) f o g b) g o f c) f o f d) g o g a. the domain of f o g is b. (g o f )(x)= a. the domain of g o f is c. ( f o f )(x)= the domain of f o f is d. ( g o g)(x)= the domain of g o g is
Consider the following function. (If an answer does not exist, enter DNE.) f(x) = x2 +...
Consider the following function. (If an answer does not exist, enter DNE.) f(x) = x2 + 5 − x (a) Find the vertical asymptote(s). (Enter your answers as a comma-separated list.) x = Find the horizontal asymptote(s). (Enter your answers as a comma-separated list.) y = (b) Find the interval where the function is increasing. (Enter your answer using interval notation. Find the interval where the function is decreasing. (Enter your answer using interval notation.) (c) Find the local maximum...
Consider the random sample X1, X2, ..., Xn coming from f(x) = e-(x-a) , x >...
Consider the random sample X1, X2, ..., Xn coming from f(x) = e-(x-a) , x > a > 0. Compare the MSEs of the estimators X(1) (minimum order statistic) and (Xbar - 1) Will rate positively
Find the domain for each function please explain. f(x)=10x^2 + x f(x)= -2/x^2
Find the domain for each function please explain. f(x)=10x^2 + x f(x)= -2/x^2
Let f(x) = 5x+3 and g(x) =2x-5. Find (f+g)(x),(f-g)(x),(fg)(x), and (f/g) (x). Give the domain of...
Let f(x) = 5x+3 and g(x) =2x-5. Find (f+g)(x),(f-g)(x),(fg)(x), and (f/g) (x). Give the domain of each. (f+g) (x) = (f-g)(x) = (fg)(x) = (f/g)(x) = The domain of f+g is_ The domain of f-g is_ The domain of fg is _ The domain of f/g is _ Please at the end provide showed work.
ADVERTISEMENT
ADVERTISEMENT
ADVERTISEMENT