tan (xy) lim = ? (x.y)→(1,0) y+xy (c) 3 (d) - (e) 1 (a) 0 (b) 114

Q: For the function f(x) = -7 e X, find f"(x), f''(0), f'"(9), and f''(-9). f"(x) = (Type an exact…

A: The objective is to solve the above question.

Q: Directions: Solve the initial value problem. y': = 9-y 1+ t 2 and y(0) = 9

A:

Q: Find y as a function of x if x*y" + 11xy + 25y = x', y(1) = -4, y(1) = 0. y =

A:

Q: For the function f(x) = 8x² + 10x + 24, find f' (x) using the f(x + h) – f(x) definition lim h→0 h…

A:

Q: -2 (a) f(1) = (b) f'(0)= -1 (c) Is f'(1.5)>0? ("yes" or "no") (d) lim h-0 f(h-1)-f(-1) h =

A: Note:As, per our guidelines we are supposed to answer only 3 subparts if there are multiple subpart…

Q: f(x) 132. Let h (x) = g(x) Find a. h' (1), b. h' (3) , and с. h' (4).

A: Given

Q: e2t – e-2t – 4t lim t-0 t – sin(t) (use L'Hospital multiple times)

A:

Q: (A) f(x) = √√√x + 2x (B) f(x) = √√√x – 2x² (C) f(x) = 2x² + √x (D) f(x) = 2x − √√x

A:

Q: Calculate the difference quotient for f(x) = 5 – x² at a = 4. (Express numbers in exact form. Use…

A:

Q: 5. Consider the function y(t) = rect (a) Sketch y(t). (b) Sketch (d+1)y(t). d-5 (c) Sketch y(t-(a +…

A: We have been given: yt=recttd+5 We have to sketch: a ytb yt-a+1c d+1ytd y2t-a+1

Q: What is the domain of the function y=sec(x+π)

A:

Q: Find f′(x) for the function: (a) ​f(x)= 3w^9-7w/5w (b) f(x)= 3x-5/x-5

A: (b). According to the question, we have to find f'x for the function fx=3x-5x-5. The derivative of a…

Q: The equation of a tangent line at a point (x₁, f (x₁)) where limh→0 f(x₁+h)-f(x₁) h = +∞ is x = x1.…

A:

Q: Let f(4) (t) denote the 4th derivative of f (t). Assume limt →00 f(3) (t) e-st = 0. Then L{f(4) (t)}…

A:

Q: For f(x) = x? – 2x – 1, find f(2), f'(2), and f(3) – f(2). - a. f(2) = -1 b. f'(2) = c. f(3) – f(2)

A:

Q: If  F (s) = L {f (t)} (s) = 3/s(s2 + 9) (image 1) Then: L -1{F(s)/ s} (t) Is equal to: (image 2)

A:

Q: f(x) Use the graphs of f and g and their tangent lines at (2, 0) to find lim x→2 g(x) У4 0 y = 1.3(x…

A: The graph of f and g and their tangent lines at (2,0) isWe have to use this graph to findWe know…

Q: Find F(s). F(s) = L {tu(t = 3)}

A: detailed solution is given below

Q: 3a) Determine the equation of the tangent to f(x) = In(3x + 4), at x = 2. %3D Equation of Tangent:…

A: Please see the explanation below

Q: Assume that ƒ′(3) = -1, g′(2) = 5, g(2) = 3, and y = ƒ(g(x)). What is y′ at x = 2?

A: Given:

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.