The cdf of a continuous RVX is given by 0, x < 0 sin(Ax) F(x) = + 6x, A 0

Q: cos (Vx)= 4x- a, Co,) 2

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Q: (a) For f(x) = x² sin(x), find a partition P of [-5, ) such that U(f, P) – L(f, P) < . Note sin() =…

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Q: 2. If f(x, y)=x² cos y-y' sin x-xe'-ye* +2x*y', show that ôxôy ôyôx

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Q: Show that the function f (x) is continuous on Sin x, r 4 -

A: You have to find the left and right hand limit for the given function.

Q: 1+12-tan-1t t2 f'(t) = t+ 0 t = 0.

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Q: .Find the estimate for the root of f(x) = sin x + cos (x² + 1) – 1using Bisection methodx, = 1. 5,…

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Q: Use integration by parts to show that, for n > 2, 1 cos a sin"-1 n 1 sin"-2 xdx. n - sin" xdx = x +…

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Q: Find a value of c that will make the following function continuous at x = 0. sin² 4x x ≤ 0 x² f(x) =…

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Q: Find the absolute extremum point(s) of f(x) = e' -Cos x on [-골, T), E any.

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Q: 3) If f is continuous everywhere and | f(x) dx = 6, find sec" 2x · f(tan 2x) dx.

A: d/dx(tanx)=sec^2x Tan (pi/4)=1

Q: The function f: x 1-> a + b cos x, is defined for 0sxs 2n. Given that f(0) = 10 and that %3D n)= 1,…

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Q: Find the intervals on which ƒ is increasing and the interval on which it is decreasing.

A: Given function is fx=9-x2+sin-1x3.

Q: What is the limit of sin when x approaches 0? Select one: O a. 1 O b. 0 O c. Does not exist

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Q: For f(x): cos(x) + 2, choose all values of c in the interval TT 37 guaranteed by Rolle's Theorem. 2'…

A: Given, fx=cosx+2 f'x=-sinx By Rolle's theorem, fx=cosx+2 is defined in the interval -π2,3π2, such…

Q: Find minimum of sin(x + 3) – sin(x + 1) – 2 cos(x + 2) where a E R.

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Q: Find дх (дхду) 6,e at the point(7,), where g(x,y) = cos(y) [sen(x) + xy].

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Q: h(z) = e sin z – sin z + cos z

A: This problem based on application of derivative.

Q: d sec z = sec z tan z dz

A: The function is a rule that associates or fixes a number to the particular point z . If , then the…

Q: It is given that f(x) = tan (1 +x). %3D Find f(0) and f '(0), and show that f "(0) = -

A: We know thatddxtan-1x=11+x2

Q: .A telegraph cable is made of an outer winding around an inner core. If x is defined as the core…

A: Using double derivative test to get max value of x

Q: .Find the estimate for the root of f(x) = sin x + cos (x² + 1) – 1using Bisection methodx, = 1.5, X…

A: Solution

Q: At which of these x-values is the value of y=cos x greater than the value of y=sin x? Select all…

A: From above we can see that when x=π6, (cos x,sin x)=32,12 here cos x&gt; sin x From above we can see…

Q: on f(z) = e cos x+ ie-Y sin x is entire.

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Q: 3. Determine any points of relative extrema of g(r) = 2 sin(x)- -r on 0, 271. %3D

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Q: If ƒ is continuous everywhere and 1| f(x) dx = 6, find | sec? 2x · f(tan 2r) dr.

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Q: Solve the problem. Suppose that fis continuous and that " H2) dz-0 and S Ka) dz = 4. Find - 60) dx .…

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Q: Given that | sec (x) dx = tan(x) + A and tan(x) dx = ln | sec(x)| + A. Show that O sec2(0) d0 = 0…

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Q: The trigonometric substitution x = = 3 sin 0 has led to the integral I = f tan³ 0 sec 0 de which can…

A: Topic:- application of integration and trigonometry ratios

Q: The value that will satisfy potentia. function p is x + y sin x None = In (x +y %3D

A: Thanks for the question :)And your upvote will be really appreciable ;)

Q: Find the critical numbers of the function: f(0) = 2 sec 0 + tan 0, 0 < 0 < 27 Remark: Use "pi" for T…

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Q: Find dy and simplify whenever possible. dx secx+tan x 1. у %3 sec x-tan x - 2. y = e-* cos e¯* – sin…

A: 1. y=secx+tanxsecx-tanx2. y=e-x cose-x-sine-x3. y=arctanx-1+x2

Q: Let f(x) Then f'(x) = 3 sin x 6 sin x + 2 cos x m = The equation of the tangent line to y = = f(x)…

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Q: d tan(2) = %3D dz sec(x) O cot(x) O sec-(z) O sec (z) tan (z) O

A: We use the standard results of derivatives.

Q: It is known that f(x) = sin(x). Estimate f'(0.6) and f''(0.6) using the 3-point central formula with…

A: Given fx=sinx and h=1 and h=0.5

Q: on [ 0, 2î] ,determine all velafive the Finction. .If f(x) = sin x t cos X extrema for

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Q: 3. If w-f(x.y) and x-r.cose, y-r.sin6 Prove that - A + fy ar

A: Given that w=f(x,y) and x=rcosθ,y=rsinθ Prove that ∂w∂r2+1r2∂w∂θ2=fx2+fy2

Q: Obtain the approximate answer for 2 cos(x )dx using the trapezoidal method so 3) that the maximum…

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Q: Find the limit of sin2x/sin3x as x approaches to 0.   a. 1 b. 1/2 c. 0 d. 2/3

A: here we must know about  L'Hopital's rule to solve the given problem which is used whenever we…

Q: Find a value of c that makes Continuous extension the function 9x - 3 sin 3x 5x f(x) = c, continuous…

A: The given function is

Q: Determine the concavity of y = 3 + sin x on [0, 27

A: Given that y=3+sinx on 0,2πTo find : concavity of function Solution : if y''=d2ydx2&gt;0 then…

Q: How many periods of the function y = sec x are there between = and 3T -

A: Given: So, from the figure, it can be observed that only one period of y=sec x is there between -π2…

Q: f(x) is a sin function with amplitute 1, and is such that f(0)=0 f(1)=0 f(x) >= 0 for x element…

A: f(x) is a sin function with amplitute 1, and is such that f(0)=0 f(1)=0 f(x) &gt;= 0 for x element…

Q: 4. Use Midpoint Rule, Trapezoid Rule, and Simpson's Rule with n =. 4 to estimate f V1+ cos a dx.

A: Given integral :

Q: A pdf is given by 2 cos (x 3 ").0<x< f(x) = 3 Show that this is a valid pdf and then find P(X<1).

A: Topic:- probability

Q: Is there a value of c that will make sin² 3x f(x) = C, x = 0 continuous at x = 0? Give reasons for…

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Q: The graph of f(x) = cos x and a tangent line to f through the origin are shown. Find the coordinates…

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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.