19. Solve for A and B so that g(x) has a limit at both x = -1 and x = 3. 4x - 2, X> 3 g(x) Ax + Bx + 2, -1< x < 3 Зх + 1, X< -1

Q: what is the maximum/minimum of: f(x)=5x3e-x on [-1,6]

A: Differentiate the given function with respect to x and find the critical points,

Q: Find the absolute maximum/minimum of function f(x) = x3 - 16x + 1 %3D

A: fx=23x3-16x+1 to find the critical points take derivative=0 ddx23x3-16x+1=0 ddx2x33-ddx16x+ddx1=0…

Q: Let f(x) = 1+ V7x +1. Determine the largest possible domain of f(x) Select one: • [-1/7, +o0)

A: Given function is  fx=1+7x+1

Q: Find the directional derivative of f(x, y) = V5x + 3y at the point (0, 2) in the direction 0 3…

A: f(x,y) = 5k+3yt point (0,2)in direction θ= 5π4 radiusto find directional derivativesolution1)…

Q: Find where f(x) = 1-ax x(x-a)(x+b) is discontinuous.

A:

Q: Let f : R → R, where f(n) = 5 . Answer the following questions. 7x²+3*

A:

Q: 2 Suppose y is a function of x such that y * and y(4) = -3. Find y. |

A: The differential equation is given by y' = 2x                                   .......(1) Initial…

Q: Show that f is linear of slope m if and only iff(x + h) - f(x) = mh (for all x and h)

A:

Q: B. Determine whether f(x) (x - 3) (2x + 1) (x + 4) is continuous at x= 3.

A:

Q: lim f(x) = 8 lim f(x) = -4 f(-6) = 5 I→-6- z-6+ lim f(x) = 2 lim f(x) = 8 f(5) = 4 z+5+ lim g(x) = 6…

A: Given  functions f(x) and g(x)

Q: Let f(x) = 8x3 - x4 + 4. 1. Find the local maximum and minimum points

A: f(x) = 8x³ - x⁴ + 4 So, f '(x) = 24x² - 4x³  &amp;, f "(x) = 48x - 12x²

Limits

When it comes to calculus, limits are considered to be a very important topic of discussion. The main importance of limit lies in expressing the value of a function as it gets closer to a certain value. Also, limits can help you to understand other topics, such as continuity and differentiability better. In a broader sense, every calculus notion is a limit. Other branches of calculus have also been derived from limits.