1. True or False. T F L; (cosx – sec x cot x + 2x7 + 4)dx = 2 f(cos x + 4)dx T. F If f'(8) exist then lim f(x) = f(8) x→8 T F If f(1) = f(4), then there is a c E (1,4) such that f'(c) = 0 (3π/4 Jn/4 T F Le sec? x dx = tan x | Зл /4 = -1-1= -2 T/4 F If f(5) is undefined, then lim f (x) does not exist. x+5 T

Q: Find the derivatives a) f(x)=√x+1 b) f(x)=sin(x+3) at a=0 c) f(x) = == X x+1 of the following…

A: Given the functions, (a) fx=x+1 at a without numerical value. (b) fx=sinx+3 at a=0. (c) fx=xx+1 at…

Q: 2. Use the definition = f'(x) = lim f(w)-f(x) to find the derivative of y = tan x. dx w-x

A: Let's take; w - x = h w = x + h As w approaches x; w-x = h →0   f'(x) = limh→0  [f(x+h) - f(x)]/(h)…

Q: Let A be an m x n matrix, and let B and C have sizes for which the indicated sums and products are…

A: If the product AB is defined, the entry in row i and column j of AB is the sum of the products of…

Q: For n 4 we find the derivative of f(x) = x* as follows: f(x + h) - f(x) (x + h)* – x lim f'(x) = lim…

A:

Q: (4) Find the derivative of f(x)= tanx+5

A:

Q: Find Integral (cos(x) cos (2x) cos (5x) dx : considering cos (mx) cos (nx)= = (cos((m-n)x)+ cos…

A:

Q: x-sinx (i) lim x2

A: i) limx->0x-sin xx2

Q: x2-8x+15 ; x 3 a) If f(x)= 2x-6 is continuous at x=3, then find the 2-5 ;x=3 value(s) of k. sinx b)…

A:

Q: (sinx -) tan*(5x) Q3/ 1)- lim, 2)- limx-0 (3sin?x -sinx +1) x sin3 (2x)

A: There are multiple question. As per Bartleby policy Kindly ask other question separately.  Given…

Q: A1) Using the definition of derivative, find the derivative of f(x) = x2 + 8x + 8.

A:

Q: The derivative of the function f(x) = elan(=) + Ve is

A:

Q: dv g) tan(x- y) = y 1+x² d 1/₂ (tan ex-x) = $x (1+x) dx dx Sec² (x-y). (1-dy) = dx Sec ³ (x-y) - dy…

A: Given query is to find the derivative.

Q: Ql:- Find the domain of the following functions a) S(x) = sin"*(2 – 3x) b) f(x) = sec"*(x – 2)

A: we have to find domain

Q: Find f" (x), given f(x) = sec x. O f" (x) = sec³ x tan x Of" (x) = sec a tanz Of" (x) = sec³ x + sec…

A:

Q: b. Determine if the lim f(x) exists, if f(x) is defined as follows: X4 12x + 3, 5x-9, x < 4 x 24…

A: Both question are solved as, follow

Q: Solve using method of undetermined coefficients: y" + y' - 2y = x². %3D

A: Solution :-

Q: 1. f(r +h)-f(r) Using f'(r) = lim %3D Find the derivative of f(r) = V3x- 4. %3D

A: To find the derivative of f(x)

Q: Find f" (x) if f (x) = tan(x² − 1). ○ 2 sec² (x² - 1) ○ 2 sec² (x² − 1) (1 + 4x² tan(x² − 1)) ○ 2…

A:

Q: ph represents the derivative function f'(x) of a function f(x). rval of increase and decrease of the…

A:

Q: 27: let f(x) = tan(x)+ sec(x) find f"(x)

A: As per our guidelines, we are allowed to answer only one question. Since you have asked multiple…

Q: Find f. f(t) = f'(t) sec(t) (sec(t) + tan(t)), -2-√2 x Need Help? Read It Watch It - 1/2 < t < 1/₁ (…

A:

Q: 2. Use the derivative rules to find f (x). (a) f(x) = (2x® – 8x-2 + 9) +) 3 (b) f(x) = COS x CSCX_…

A: Find the derivative

Q: The definition of the derivative of a function is f'(x) = lim f(x + h) – f(x) h→0 h Write, but do…

A: Given: The definition of the derivative of a function is f'x=limh→0fx+h−fxh I. fx=2xsinx II.…

Q: d dx [ 3+√√f(sin( sin(x)) cos(x) f' (sin(x)) 2√f(sin(x))

A:

Q: Find the derivative (dy/dx) of the following functions: I) y = (sin x + cos x) sec x

A: Since there are multiple questions present, according to company policy we will be answering only…

Q: Find the discontinuities, if any.  f(x) = sin (x^2 - 2)  f(x) = sec x lim    sin θ / θ2 θ→0+

A:

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.