х If f(x) = then calculate f Enter the numeric answer into the textbox. If the...
5. Let f R2 ->R2 be the function given by f(x, y) (х + у, х — у). (i) Prove that f is linear as a function from R2 to R2. (ii) Calculatee the matrix of f. (iii) Prove that f is a one-to-one function whose range is R2. Deduce that f has an inverse function and calculate it. (iv) If C is the square in R2 given by C = [0,1] x [0, 1], find the set f(C), illustrating...
Consider the following function. (If an answer does not exist, enter UN 36 f(x) = x + х (a) Find the intervals where the function is increasing and where it is decreasing. (Enter your answer using interval notation.) increasing decreasing (b) Find the relative extrema of F. relative maximum (X,Y) - relative minimum (X,Y) - (c) Find the intervals where the graph of fis concave upward and where it is concave downward. (Enter your answer using interval notation.) concave upward...
1) Allow f(x) = x3, and g(x) = 2x. Determine f(g(1)). 2) Enter the formula for a sine function with an amplitude of 5, a period of 90 degrees, a shift of 45 degrees to the right and 3 units upwards. Determine the exact value of the expression sin (v) + cos (v) given that tan (v) = 7/3. 3) Solve the equations in the range 180≤x≤360 degrees. Answer with one decimal. a) tan (x) = 3.2 (I would like...
sin x 5. (10 marks) Check whether f(x) = х if x = 0 if x = 0 is differentiable at x=0. Prove it using an ε - 8 1 proof.
3л If cos x = - , and < x < , what is sin(x + )? Enter your answer as a fraction in simplest form, like this: 3/14
Consider the following function. f(x) = cos(x) - sin(x), (0, 2) (a) Find the critical numbers of f, if any. (Enter your answers as a comma-separated list.) (b) Find the open intervals on which the function is increasing or decreasing (Enter your answers using interval notation. If an answer does not exist, enter DNE.) increasing х decreasing X (c) Apply the First Derivative Test to identify all relative extrema. (If an answer does not exist, enter DNE.) relative minimum (X,Y)...
Calculate the osmolarity of 0.39 M NaCO solution. Submit numeric answer only with correct number of sig figs. (example: If your answer is 2.6 osmol, your answer should look like 2.6EO) Respond with the correct number of significant figures in die and only i t before decimale 2.50 for 25x10 aide Numeric Answer
Find f'(x) f(x) = x х Consider the function f(x) = 5x + x Bx a. Find f'(x) b. Find the x-values where the tangent line is horizontal Use the product rule to differentiate. Do Not Simplify y = (7x4 - x + 2)(x5 + 4)
Previous Problem Problem List Next Problem 3 sin(x) x2 (1 point) Find lim 10 х Enter I for o, -I for -o, and DNE if the limit does not exist. Answer: Preview My Answers Submit Answers You have attempted this problem 0 times. You have attemate van
Refer to the graph of y=f(x)=x2 + x shown. Answer parts A-D as an integer or simplified fraction. a) Find the slope of the secant line joining (2, f(2)) and (4, f(4)). b) Find the slope of the secant line joining (2, f(2)) and (2+h, f(2 + h)). c) Find the slope of the graph at (2, f(2)). d) Find the equation of the tangent line to the graph at (2, f(2)). 18- 16- 14 12 10- 8- 6- 49...