number8 (6x²-1 xSl. a. DNE b. O c. 3 d. -3 e. 00 Given the piecewise...
For the piecewise linear function, find (a) f-3), (b) -2), (c) K0), (d) f(2), and (e) f(5) 2x ifxs-2 fix): x-2 ifx-2 (a) -3) (b) f-2)= (c) f(0)= (d) (2)= (e) 5)-
Please solve this problem completely. (1) Length of graphs a) Let a path C be given by the graph of y - g(x), a b, with a piecewise C function g : [a,b] → R. Show that the path integral of a continuous function f : R2 → R over the path C is b) Let g: a bR be a piecewise Cl function. The length of the graph of g on (t, g(t)). Show that [a,b] is defined as...
Use the Chain Rule and the fact that d (r)-L,o find the derivative of (b) Rewrite f(x) as a piecewise function not involving the absolute value function. (c) Find the first and second derivatives of f(x),using your piecewise function. (d) Would you want to find" without the function's piecewise representation? 2. A square and a triangle are to be cut from a piece of fabric 1 metre square, as shown Find the length which minimises the removed area ar Use...
Please solve these three questions! (1) Length of graphs a) Let a path C be given by the graph of y g(x), a 3 < b, with a piecewise C1 function g : [a, b - IR. Show that the path integral of a continuous function f: IR2- R over the path C is b) Let g : [a, b] - IR be a piecewise C1 function. The length of the graph of g on (t, g(t)). Show that [a,b]...
Given the piecewise-defined function below, what is f(1)? fly 19-x² for x<3 1 x+3 for x 23 7 A. B. C. D. 4 8
part (c) 7.23. Let y(x) = n²x e-nx. (a) Show that lim, - fn(x)=0 for all x > 0. (Hint: Treat x = 0 as for x > 0 you can use L'Hospital's rule (Theorem A.11) - but remember that n is the variable, not x.) (b) Find lim - So fn(x)dx. (Hint: The answer is not 0.) (c) Why doesn't your answer to part (b) violate Proposition 7.27 Proposition 7.27. Suppose f. : G C is continuous, for n...
Question 1(a&b) Question 3 (a,b,c,d) QUESTION 1 (15 MARKS) Let X and Y be continuous random variables with joint probability density function 6e.de +3,, х, у z 0 otherwise f(x, y 0 Determine whether or not X and Y are independent. (9 marks) a) b) Find P(x> Y). Show how you get the limits for X and Y (6 marks) QUESTION 3 (19 MARKS) Let f(x, x.) = 2x, , o x, sk: O a) Find k xsl and f(x,...
Problem 6.8. Let X = {1, 2, 3}, Y = {a, b, c, d, e}. (a) Let f : X → Y be a function, given by f(1) = a, f(2) = b, f(3) = c. Prove there exists a function g : Y → X such that g ◦f = id X . Is g the inverse function to f? (Hint: define g on f(X) to make g ◦ f = id X . Then define g on Y...
se of thelr connection with secant lines, tangents, and instantaneous rates, limits of the form with Because o 12-E occur frequently in calculus. Evaluate this limit for the given value of x and function f. 31) fx)-5x2-5,x A) -15 31) BDoes not exist Differentiate the function and find the slope of the tangent line at the given value of the in -10 D) 5 32) s--44-53, t-1 A)-1 D) 1 C) 31 B)-31 Find the indicated derivative. 33) 33) Find...
Graph the piecewise function. (Apts) -8²+2 13. h(x) ix-21 If 1<x<3 -6 if x 25 b. Where is h(x) increasing? (Ipt each) c. Where is h(x) decreasing? d. Is there an x-intercept, if so where? e. Is there a y-intercept, if so where?