Question

In: Math

A. Let f(x) be: x+(12/(1-x)) if x is less than or equal to -3 x+3 if...

A. Let f(x) be:

x+(12/(1-x)) if x is less than or equal to -3

x+3 if -3 < x and x is less than or equal to zero

ln(x) if 0< x is less than equal to 5

(x-5)/5+ln5 if x>5

answer and explain these answers

B. Is f differentialble at x=5? justify your answer by evaluating the one sided limits of

lim as x approches 5 (f(x)-f(5))/x-5

Solutions

Expert Solution


Related Solutions

Let [x] be the greatest integer less than or equal to x. Then at which of the following point(s) the function f(x) = x cos (π(x + [x])) is discontinuous?
Let [x] be the greatest integer less than or equal to x. Then at which of the following point(s) the function f(x) = x cos (π(x + [x])) is discontinuous? (a) x = 2 (b) x = 0 (c) x = 1 (d) x = -1    
prove that 2/pi is less than or equal to (sinx)/x which is less than or equal...
prove that 2/pi is less than or equal to (sinx)/x which is less than or equal to 1. for x is in (0,pi/2]
solve tan^2 x =1 where x is more than or equal to 0 but x is less than or equal to pi
solev tan^2 x =1 where x is more than or equal to 0 but x is less than or equal to pi
Let V be the 3-dimensional vector space of all polynomials of order less than or equal...
Let V be the 3-dimensional vector space of all polynomials of order less than or equal to 2 with real coefficients. (a) Show that the function B: V ×V →R given by B(f,g) = f(−1)g(−1) + f(0)g(0) + f(1)g(1) is an inner product and write out its Gram matrix with respect to the basis (1,t,t2). DO NOT COPY YOUR SOLUTION FROM OTHER SOLUTIONS
Let f(x) = x^3. Find a value "C" between x=0 and x=12 such that the average...
Let f(x) = x^3. Find a value "C" between x=0 and x=12 such that the average rate of change of f(x) from x=0 to x=12 is equal to the instantaneous rate of change of f(x) at x=C
3. Let X = {1, 2, 3, 4}. Let F be the set of all functions...
3. Let X = {1, 2, 3, 4}. Let F be the set of all functions from X to X. For any relation R on X, define a relation S on F by: for all f, g ∈ F, f S g if and only if there exists x ∈ X so that f(x)Rg(x). For each of the following statements, prove or disprove the statement. (a) For all relations R on X, if R is reflexive then S is reflexive....
Let f(x)=(x^2+1)*(2x-3) Find the equation of the line tangent to the graph of f(x) at x=3....
Let f(x)=(x^2+1)*(2x-3) Find the equation of the line tangent to the graph of f(x) at x=3. Find the value(s) of x where the tangent line is horizontal.
Let f(x) = x^3 − x on [−1, 1]. Find the true area of the shaded...
Let f(x) = x^3 − x on [−1, 1]. Find the true area of the shaded region using a limit of Riemann sums, taking the sample points to be the left endpoints. Hint: to ease the computations, you can use the fact that (a + b)^ 3 = a ^3 + 3a^2 b + 3ab^2 + b^3 (which follows by expanding the cube). Verify your work by evaluating the corresponding definite integral using the FTC.
Let P2 be the vector space of all polynomials of degree less than or equal to...
Let P2 be the vector space of all polynomials of degree less than or equal to 2. (i) Show that {x + 1, x2 + x, x − 1} is a basis for P2. (ii) Define a transformation L from P2 into P2 by: L(f) = (xf)'    . In other words, L acts on the polynomial f(x) by first multiplying the function by x, then differentiating. The result is another polynomial in P2. Prove that L is a linear transformation....
The density of a random variable X is given by f(x)=(3x^2, o less than x less...
The density of a random variable X is given by f(x)=(3x^2, o less than x less than 1, or f(x)=0, otherwise Let Y=e^x (a) find the density function of Y(b) find E(Y) two ways:(i)using the density of Y and (ii) using the density of X
ADVERTISEMENT
ADVERTISEMENT
ADVERTISEMENT