Find all the antiderivatives of the following function. Check your work by taking the derivative. H(z)...
Find all the antiderivatives of the following function. Check your work by taking the derivative. f(x) = 19 ex The antiderivatives of f(x) = 19 e* are F(x) =
4. (a) A function f has first derivative f (r) - and second derivative f"(z) It is also known that the function f has r-intercept at (-3,0), and a y-intercept at (0,0) (i) Find all critical points, and use them to identify the intervals over which you will examine the behaviour of the first derivative (ii) Use the f'(x), and the First Derivative Test to classify each critical point. (iii) Use the second derivative to examine the concavity around critical...
Step 6 So ultimately the crux of the matter is to find antiderivatives for these two functions The former is one you should already have an idea for (from your experience with calculating derivatives of inverse trigonometric functions). The latter is analogous, but can be dealt with by a useful trick you may have seen in precalculus: Find real numbers A and B to make this true, then use it to give an antiderivative for Notes on polynomial division will...
2 (5). Find the following antiderivatives. (a) l' z*d (n) [(e* – 2sin 2)der
Hw2 Q1 Show that the function f(z) = z2 + z is analytic. Also find its derivative. (Hint: check CR Equations for Analyticity, and then proceed finding the derivative as shown in video 8 by any of the two rules shown in video 7] Q2 Verify that the following functions are harmonic i. u = x2 - y2 + 2x - y. ii. v=e* cos y. Q3 Verify that the given function is harmonic, and find the harmonic conjugate function...
answer all thee questions with work!!! please and Thank you (1) Find the derivative of each of the following functions: (a) f(t) = ln(3-cost) (6) gle) = VERA (2) (a) Find the linear approximation to y-Vaata 81. (b) Use your answer in (a) to approximate V80. (All work must be shown it is not enough to put this into a calculator!) (3) Find the absolute maximum and minimum of the function h(x) = x + on the interval (0.1, 4).
(a) A function / has first derivative f'(z) = and second derivative 3) f"(x) It is also known that the function f has r-intercept at (-3,0), and a y-intercept at (0,0) (i) Find all critical points, and use them to identify the intervals over which you will examine the behaviour of the first derivative ii) Use the f'(), and the First Derivative Test to classify each critical point. (ii) Use the second derivative to examine the concavity around critical points...
5x + 1 Use the definition of the derivative to find the derivative of the function f(x) = *-*2. Then find all x-values (if any) where the tangent line is horizontal. If the tangent line is horizontal for all X, write R for your answer. If the tangent line is never horizontal, write None for your answer Answer 3 Points Keypad 11 1'(x) = 2 Tangent is horizontal at x = Prev Nex If f(3) = -1, f(3) = 17,...
Find the derivative of the function. h(x) = (x?- 1)
- 2X1 - 2M h C2X ng the following definition of a 18. Find the derivative [f'(x)] of the function f( derivative: f(x+h)-f(x) P(x) =" + tumb* (x2+2x1h+ h2) Page 6 of 7 7x + 2 x ht! h² Ś3