1 Calculate the following (possibly infinite) limits or show that they do not exist. Hint: Recall the differnece of squares property a2 – 62 = (a + b)(a – b) and that tan(x) can be written in terms of sin(x) and cos(x). x² – 49 (a) lim 7 x2 - 8x +7 sin(x) (b) lim 20 tan(x)

Q: 2.2 y = (x³ − 1)(x² − 2x + 1) using the product rule. √1 + tan² x 2.3 y= sec² x

A: solution of the given question is like aS:

Q: a) Find the limits of the following functions: i. sin 2x lim o 2x +x V+ 12-4 lim X-2 x- 2

A: To find the limits of the following functions : (i)  limx → 0 sin 2x2x2 + x(ii)  limx → 2 x2 + 12…

Q: Suppose we define a function f(x) by f(x) = a1 sin(x) + a2 sin(2x) +· + an sin(nx), .. for constants…

A:

Q: Find the value of the following and justify your result. (a) lim | [(4x – 3) sin(æ)]/2n-1 dax (b)…

A:

Q: 2. If f(g(x)) = sin x + 3sinx - 1, determine possible expressions for f(x) and g(x), where g(x) # x.

A: (1st method/way): Let f(x)=x²+3x-1 and g(x)=sinx Then we can find f(g(x)) as follows…

Q: 1 2. lim cOs X -

A: The given function rewrite as

Q: C. lim x→1+ 5x 4 31 -1-x 3x]

A:

Q: b. lim cos(x)-1 x2

A:

Q: A. Let 0 = 2x, then the identity cos 2x = 1-2 sin2 x becomes cos e = 1–2 sin2 (0/2). a. Use this…

A:

Q: 16. Evaluate ft tan5 x sec¹ xdx.

A: We know that Sec²x = 1+ tan²x ∫ xn dx=( xn+1)/(n+1)

Q: 5x C. lim 1-52, x→1+ -1-x 3x] D. Compute the derivtive of sin³ (x + 1)

A: Given: sin3x+1. We have to compute the derivative of the given function.

Q: Evaluate these two limits given below

A: We will find the limits.

Q: 1. If f(x) = sinx, show that f(x + y)-f(x) = cos x siny - 2 sin x sin² 2 2Y-T

A: 1) Given f(x)=sin(x)

Q: Please

A: To find:

Q: Use the figures to evaluate each function given that f(x)=sinx,g(x)=cosx, and h(x)= tan x. g (α /2 )

A: gx=cosx. Since the x-coordinate of any point on the unit circle is the cosine value, therefore…

Q: for f (x) = cosx + sinx function; (Table attached in to description) table is given. a) Find the…

A:

Q: (a) lim r0o In(x² + 5) In(x + 2) (b) lim(1+3 sin x)/ª. 2 cos x - (c) lim r1/4 1- tan x

A: I use L hospital's Rule

Q: Expand the following functions in terms of Legendre polynomials: (a) 35 (cos 0)4 (b) cos0 - (cos)³…

A: As per the norms, we will be answering the first three subparts. So, if you need an answer to others…

Q: 2. Which function is shown on the graph below? -2 A. S(x) = tan 1¹ (x-7) - B. /(x) = tan-1/(x+4)-2…

A:

Q: (c) (z-a)", where a EC and n = N*

A:

Q: Consider the function f(x) = cos(x2 - 2) + 1 on the interval (-3,3). Calculate the two x-intercepts…

A: f(x)=cos(x2-2)+10=cos(x2-2)+1cos(x2-2)=-1 As we already know, the solution to the trigonometric…

Q: a) f(x) = 1+ Sinx b) f(x) = x² + 2x- 1 c) f(x) = 2* + 2 for all x eR for all x eR for all x eR

A: Given function are: [1] f(x) = 1 + Sinx   for all x ∈R [2] f(x) = x2 + 2x - 1  for all x ∈R [3] f(x)…

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.