-0.03 -0.02 -0.01 -0.007 0.007 0.01 0.02 0.03 sin x f(x) = 2r? -0.9433 -0.9615 -0.9804 -0.9862 -1.014 -1.02 -1.042 -1.064 et – tan x g(x) = 1.0014 1.0006 1.0002 1.0001 1.0001 1.0001 1.0006 1.0013 cos² x 鸣f) X-

Q: Find the value of x in degrees: sin x = 0.8766

A: The sine function is positive in the first and second quadrant. We can use inverse sine function to…

Q: 20 What is the frequency of the periodic function f(0) =2 tan()? O 2 5 sin(-), What is the frequency…

A: Given f(θ) = 2 tan(2θ/3) Frequency of tan θ is 1 For f(θ) period is  π/(2/3) = 3π/2 Frequency is…

Q: Find the periodic function f(x) = sinx + tan-+ sin- X + 23 + sin 2n+1 + tan ... 2n

A:

Q: sin 0 + In + 22+3 = -3 - cos 20 - In y? + 327-4 = + 2ln y+ 22 -3 1+ (cot 0)2

A: Given system is sinθ+ln1y+2z+3=-3 lny2+32z-4=1-cos2θ2 21+cotθ2+2lny+2z=-3

Q: h(x) = tan x - tan-x h(x) = 3 sec-1x h(x) = 14 cot x + 12 cos-x h(x) = (3x? + x - 1) csc-x %3D

A: “Since you have posted a question with multiple sub-parts, we will solve first three subparts for…

Q: 10- Sin'x- cos'x is equal to: a)2x b)1 c)-1

A: 10-sin^2(x) -cos^2(x) We apply trigonometry rule

Q: 2. True or False. The dx [Arctan(tan x)] = 1 for all x in the domain. ans. True

A:

Q: The slope of the tangent line to the curve at the point where x = O +1 -1 DNE f(x) = sin² x cos²x

A: The slope of the tangent line to the curve  y = f(x) at the point x= k is f '(k)

Q: 1. Find the exact values of sinh (0) and cosh (0) using their definitions.

A: Sinh x=ex-e-x2∴ sinh0=e0-e-02=1-12=0∴sinh0=0      cashx=ex+e-x2∴cash0=e0+e-02=1+12=1⇒cash0=1

Q: Let f(x) = 8 cos x + 5 tan æ f'(x) =-8 sin(z) + cos(z)2 r(#) = 37 Find the exact trig values for…

A: Since, we have been given that f(x)=8 cos (x)+5 tan (x)Also, we have f'(x)=-8 sin (x)+5cos (x)2Our…

Q: On the graph of f(x)=tanx and the interval [0,2π), for what value of x does the graph meet the…

A: x 0 π4 3π4 π2 π 5π4 3π2 7π4     tanx 0 1 3 ∞ 0 -1 -∞ -3

Q: If x = 3 sin(0), then а. V9 + x? cos(8) 3 b. cos(x) Vx2 + 9 C. tan(x) d. cot(x) = 3 || е. sec(x) 3 O…

A:

Q: -1 We can conclude from the derivative of sin-1(x)and cos-1(x) that sin-(x) + cos¯(x) is constant.…

A: Explanation: find the derivative of sin-1x & cos-1x

Q: 68) Find a value of c that will make sin2 4x 0 x2 f(x) = C, x 0 continuous atx = 0.

A: Given,

Q: 11. y = coS x COS X -2 tan x 12. y = x? sin x tan x 13. у %3D 1 14. y = --3 sin x 15. y = x cot x

A:

Q: can you prove it, please ? cosh 2x=sinh^2x+1 = 2 cosh^2-1

A:

Q: If cos x is replaced by 1 - (x2/2) and |x |<0.5, what estimate can be made of the error? Does 1 -…

A: We’ll answer the second question first. Notice the question have used first two digits of Maclaurin…

Q: -- cos( sin-!x) + C 1-x² A True B) False

A: SOLUTION-

Q: -sin (In x?)ecos² (In x) dx 100x2-x2e2 cos (In x)

A:

Q: 2. Apply the properties of even and odd functions to find the exact va a. sin(-120°) (-#) c. sin…

A:

Q: sech? (In x²) 15. f x/6 tanh (In x²) – tanh² (In x²) dx

A: I = ∫ sec h2 (ln x2)x6tan h(ln x2)-tan h2(ln x2)dx=∫ sec h2(2ln x)x6tan h(ln x2)-tan h2(ln x2) dx=∫…

Q: 2x, given tan x= 2 and cos x is less than 0

A: Given tan x = 2 and cos x < 0.

Q: Evaluate (cos x In sin x) dx. Select the correct response: O cos x (In sin x-1) +C sin x (In cos…

A:

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…

A:

Q: Compare the accuracies of the approximations sin x = x 6x/(6 + x²) by comparing the graphs of and…

A: Calculate the approximate value of f(x).

Q: (2 cos 2x+ 3 sin 2.x) 7. evaluated at x = 1 rad

A: Given query is to find the value of the expression at x = 1.

Q: cos? (x) 5 x²e* 6 V1 – x³ 4 - ex 7 sinh(x) 8 x² arctan(x) 9 1- X

A:

Q: [cos x - sin x 0] cos x 1] 5. If f(x) = | sin x 0|, show that f (a)f(b) = f(a + b).

A: f(x)=cosx-sinx0sinxcosx0001

Q: Establish each identity given in attachment.

A: To establish the identity: lntanθ=lnsinθ-lncosθ Solution: We know that, tanθ=sinθcosθ Property of…

Q: x² + 9 dx J x2 – 1)(x² + 4) | In \x + 1| + In |x – 1| +; tan-1 (-) + c -In |x + 1| - In |x – 1| -;…

A: Topic:- application of integration

Q: The derivative of In (cos x) is A -tan x B None of the given choices tan x D sec x -sec x

A:

Q: The first derivative of the function h is given by h' (x) = 3 ln(2 + cos(2x)) x, and the second -6…

A: Given: h'(x)=3 ln2+cos2x-xh''(x)=-6sin2x2+cos2x-1-2&lt;x&lt;2

Q: 4,5in3x =sinx S Sinx(sin?x-\= sin?x. Sinx(sinx-1). COS X tank (sin zx - COS tan-o TT

A:

Q: Find all values of x in the interval [0, 2π] that satisfy the equation.  sin x = tan x

A:

Q: xy2-cos x sin x y' = ху?-со -cOs x sin У(1-x?)

A:

Q: Refer to the graph of y = sin x or y = cos x to find the exact values of x in the interval [0, 4p]…

A: Sketch the graph of function y=sinx as shown below.

Q: Find a root of f(x) = 6 Sin (x)e- x + 1 using Newton Raphson Method accurate to 5 decimal places.

A:

Q: Suppose y=sin x, what is x-value between 2pi and 4 pi corresponding to y-value of -1

A:

Q: Find the linear approximation of f(x)=sin(x) at x=3π4 and use it to approximate sin(134∘). Give…

A:

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

A:

Q: sin x and coS x are periodic functions with period Tt. True False

A: Given statement is "sinx and cosx are periodic functions with period π."

Q: Cos (GX) = Cos 15°, 0°<x < 360° Со X) = Cos 15°, O° < x < 360° %3D Tan( x ) = tan,05x < 2n )= tan,

A: We can find the answers as below

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+…

A:

Q: 1. Given tanx = - and cos x >0, find secx. A. в. C. V10 D. 2V10 2. Given secx and sin x 0. 3. Find…

A:

Q: If f (x) = - sin(x), then f (10) (x) is equal to = - sin(x), thenf (10) (x) is equal to A - sin(x) B…

A:

Q: Where does the periodic function ƒ(x) = 2e^(sin (x/2)) take on its extreme values and what are these…

A: Given,

Q: Find the linear approximation of f(x)=sin(x) at x=2π3 and use it to approximate sin(121∘). Give…

A:

Q: 1. (a). Find the linear approximation to f(x) = sin x at = 0, (b). use it to approximate sin(-0.01).…

A: We have to find the linear approximation and percentage error.

Q: Identify the correct form of the indefinite integral tan (x) csc (x) dx sec-/(x) +C O tan-(x) + C…

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.