1- tan lim 2I- sin.x] (x 1+ tan x O 1/32 O 1/8

Q: Solve

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Q: If f(x) = cos x – 7 tan æ, then f'(z) -sin( x ) – 7 sec²(x) = f'(2) =

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Q: 1-cos (x-7) lim ثم اختر الاجابة الصحيحة؟ أحسب الغاية التالية xt (x-n)sin (x-7)

A: We will use the limit theorems to evaluate the limit as x tends to π.

Q: 1-cos x lim sin x x→0

A: Given: limx→01-cosxsinx

Q: -1 3. Show that sin-¹x = tan X √1-x² if |x| < 1.

A: Introduction: When there are trigonometric functions present in an expression or equation,…

Q: The largest value of the non-negative integer a for which lim x →1 - ax + sin(x - 1) + a x + sin(x −…

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Q: 1 o. = 0. Show that lim x² sin -| *

A: Use the property that -1≤siny≤1. Take y=1x, then -1≤sin1x≤1

Q: The value of lim sin x- cos x 1s 2 sin x+3 cosx

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Q: Lan: prove (:) - - 4. sin x tan =1- cos x

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Q: 14. lim cos x 15. lim cos(x+ sin 16. lim

A: If any function is continuous within a given interval, then its limit must exist in that interval.…

Q: 1 lim x? sin 1-cos³ x lim X→0 sin² x csc? x-2 lim п cotx-1 4

A: L'hospital rule: If limx→cf(x)g(x)=00 or ∞∞, then limx→cf(x)g(x)=limx→cf'(x)g'(x). Limit formula:…

Q: 1+3x- cOs x 2.) lim tan x

A: In this question we need to find limit of the given function.

Q: (a) i) Prove that 1 sin20 1 tane 1+ sin20 1+ tane for 0<0 <- 4 ii) Hence, show that the exact value…

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Q: Prove the identity.   (cosh x + sinh x)n = cosh nx + sinh nx  (n is any real number)

A: The cosh x and sinh x are given by, LHS =

Q: A tangent reduction formula Prove that for positive integers n + 1, tan"-lx - Jun-sdt. tan“ x dx n -…

A: Given tangent reduction formula is: ∫tann x dx=tann-1 xn-1-∫tann-2 x dx We have to find the integral…

Q: lim as x approches 0 of cos(6theta)-1/sin(7theta)

A: Given: fθ=limθ→0cos6θ-1sin7θ Apply limit by substituting θ=0 in the above expression.…

Q: sin 3x 1. lim x0 tan 4x 1-cos 2x 2. lim X-0 sin 2x x2-x+ 3. lim 5 X-00

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Q: find 49. lim 0 - sin 0 cos e tan 0 - 0 sin 3x - 3x + x² 50. lim sin x sin 2r

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Q: 1+sin x sin x <x<0 6 -- If f(x) = {b , x = 0 is continuous at x = 0, find the values of a and b. tan…

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Q: 3-f(x) = tanh¯1(cos(e*))

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Q: 1 1 Prove -2 secx tan x 1+ sin x 1- sin x

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Q: 3. sin(3x) = 3s in x – 4sin³ x

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Q: Evaluate the limit.

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Q: * Find the value of Tx³ + 2. lim [sin (- x3+1] -1 O

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Q: 1-cos 2x sin² x limx-0

A: Since you have posted multiple questions, as per our policy we will answer first question. Please…

Q: In(sin 4x) \ In(sin 8x) lim x → 0

A: We have to evaluate the limitlimx→0ln(sin4x)ln(sin8x)

Q: Find lim n→∞ n + cos(x) Jo ne + sin(x) So -dr.

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Q: - sin sin -y = sin (x+y) Prove that cos Xcos 4 -y 4 -x sin 4 X - 4

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Q: 1-sin 0. (5) lim cos.20 (x2-2х+1)50 (6) lim X-00 (х+5)100

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Q: 4.) Prove: sin 2x a) 2cos? x = tan x b) sin 3x = 3 sin x – 4sin3 x [Hint: sin 3x = sin(2x + x)] -

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Q: 1 + X tanh (x) 1 In 2 - 1 - X

A: The solution is given as

Q: tanx 4 – lim 0 Cos[1– –] X 0.7 O 1.5 O 0.5

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Q: 1+3x COS x - 2.) lim tan x

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Q: 1– tan(*,) [1– sin x] lim 1+ tan(x (¥2) [z – 2x] x- - 2 1/8 1/32

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Q: 1- tan lim 1– tan(*,) [1– sin.x] sin x] (2, x→| (¥2)[[7 – 2x} n – 1+ tan(x 1/32 O 1/8

A: The given expression is limx→21-tanx21-sin x1+tanx2π-2x3.

Q: Find f'(x), if f(x)= tan² 4.x. Find f'(x), if f(x) = sin² 2x./cos 2x . Find f"(x), if f (x)= Inx+…

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Q: lim,-o-cos(2.x) →0°sin²(3x) Q6- Evaluate:

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Q: Example : Find an approximation to zero of tan(nx) – 6 = 0, in [0, 0.48]by Secant Method.

A: To approximate the zero of f(x) using secant method.

Q: 1 lim, (e** - 1)sin-+9cos x . x0

A: Given: limx→0ex2-1sin1x+9cosx we know that  limx→0ex2-1=0 and  limx→0sin1x=-1 to 1 so,…

Q: Evaluate lim,→0 ela-cos 7x 8 sin x 7

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Q: (1- cos.x)? cosx) limx-0 x sin(x2)

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Q: 1-cos(2x) tan x-sin x Q6- Evaluate: a- limx-0 b- lim x-0 sin (3x) sin³x

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Q: tan(3z) lim 5z z-0 sin(n)(1-cos(h)) lim h-0 sin(h)(1-cos(h) lim h-0 h3

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Q: 1. Evaluate 2. Evaluate sin(20) 30 x-2x cos x sin x limo lim, 0

A: Given is  limθ→0sin(2θ)3θ. L'Hospital rule: limx→af(x)g(x)=limx→af'(x)g'(x) NOTE: According to the…

Q: (2) elnx = x (1) sin-1x = V1-x2 (1) ax A- Show that : cos x (2) lim x- cosx (2) (1) limx-0 В- Find :

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Q: ´1-cos x 1-cos³ 11. lim sin? x

A: The given data is limx→01-cos3xsin2x Here we use L-Hospital's rule and the L-Hospital's Rule states…

Q: a. Show that y = tan u increases on every open interval in its domain. b. If the conclusion in part…

A: (a)  Given,

Q: 3. Given f(x) = cot(x) sin(x) and g(x) = cos³(-x)(sec² (x)-1) sin² (x) a. Prove that f(x) = g(x).…

A: Given that,  fx=cotxsinx and gx=cos3-xsec2x-1sin2x

Contingency Table

A contingency table can be defined as the visual representation of the relationship between two or more categorical variables that can be evaluated and registered. It is a categorical version of the scatterplot, which is used to investigate the linear relationship between two variables. A contingency table is indeed a type of frequency distribution table that displays two variables at the same time.

Binomial Distribution

Binomial is an algebraic expression of the sum or the difference of two terms. Before knowing about binomial distribution, we must know about the binomial theorem.