f is odd, J'(x) |for æ > 2, f"(x) > 0 for 0 < x < 3, O for 0 < x< 2, f"(x) < 0 for x > 3, lim f(x) = -2

Q: \S(cos x)dx = 0 %3D

A: Let us consider f is continuous even function. Let f=x2 So, fcosx=cosx2=cos2x…

Q: , X= sin ztS d= In Find dw 2- Cost

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Q: Find the maximum and minimum valucs of f(x) = sin x + cos x on (0, 2n].

A: Given function:                      f(x) = sin x + cos x,   x∈[0, 2π] Use the second derivative…

Q: 5 Find a limit equal to In(2x – 1) dx.

A: We know that, ∫lnxdx=xlnx-x+C…

Q: -Vx+ 1+ In(x) e* lim + sin (x)cos(x)

A: Find the limit

Q: 1- Find the equation of the tangent to the curve y = 2 sin x+ cos2x at the point x = n. 2- Find the…

A: Solution:

Q: Find the limit of sin Ø/Ø as approaches 0°. * 00 1 -1 ООО

A: Using formula.

Q: The area under the entire curve is given by 15 dx. We have 00 15x-3 dx lim 15x-3 dx - lim - 00 lim…

A: The area under the entire curve is given by  ∫1x15x3dx

Q: Does the graph of the function y = tan x - x have any horizontal tangents in the interval 0 sx s2n?…

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Q: f(x)% 3D tanh In(2x) is equivalent to

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Q: 3G)Ú) Show that the reduction formula for atanx で-u sec"x dx = Sec" 「キu ) Hence use tthe formula to…

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Q: Evaluate the definite integral: r1 arctan x dx = x2 +1 0.

A: To solve the integral first I have make a substitution so that integral become easy and the solved…

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

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Q: 2. What is the largest possible area of a triangle with its base on the x-axis between x= 0 and…

A: The given curve is y=sinx. To find the largest possible area of the triangle with its base on the…

Q: If f(x) = A B (C) tanx S 0 sec ³x 1+e tanx 1+tan²x 1+ e tanx 1+12 sec²x 1+e tanx In (coor) 1+ e'…

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Q: limit x to 0 sin(4t)sec(1000t)/10t

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Q: Find lim t→ 1 1 - cos2 Int 0(0.20 를 를) 0 O t ./t+7, t-1 t2 − 1

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Q: 1: A)find the length of the curve y=3(x)/2 – 1 from x=0 to x=1 ? B) Prove that: cosh (x + y) = coshx…

A: A) Length of the curve is y=3x32-1 B) Trigonometric function

Q: Find the tangent line to the curve x cos y + y cos x = 1 at (0,1). O A. (cos 1)æ + y = 1 O B. x + y…

A: We can find the tangent line as below

Q: 1. If y=tanx, prove that y=2(y² +1)(3y² +1).

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Q: dy Cos(3x) + (In x)

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Q: th of the curve y= ln(sin x) from x = 0 to x=.

A:

Q: Q1- Prove that coth x = 2 csch 2x + tanh x %3D

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Q: 1- for y= sech x is equal to: dx a) sech' x tanh x b) 3sech sech tanh x c)-3sech2x sechx tanhx

A: Note: Since you have asked multiple question, we will solve the first question for you. If you want…

Q: S2ta J 2tan x In (cos x) dx=

A:

Q: Use the trapezoidal rule withn = 5 to approximate 4 cos(x) -dx

A: To approximate : ∫14cosxxdx using Trapezoidal rule with n=5

Q: 1. Use the delta method, 2 BONUS MARKS y = 5x² dy dx = lim h-0 f(x+h)-f(x) h to find dx for the…

A:

Q: Evaluate the integral. π f(x) dx   0   where    f(x) =    sin(x)    if  0 ≤ x <  π 2 cos(x)    if…

A: we need to evaluate the integral of πf(x).dx given that  f(x)=sinx if 0≤x≤π/2       cosx if π/2 ≤x…

Q: Find the length of y = ln (sec x) between x = 0 to x = π/4.

A: you meant to find the arc length of y=ln(secx). the formula for the length of the arc in the given…

Q: 3) Consider the fonction (a) The tangent plare to the graph of fCx,y) at the point Co,0) is (b) At…

A:

Q: Q3: Find lim,- (2 – sin –) إجابتك :Q4 For (3x³ – 5x) V2x+1 find dy/dx at x=0 إجابتك

A: Explanation of the solution is given below...

Q: find the limit as x approaches 0. 12sin(3x)/1-cos(3x) = as x approaches 0

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Q: 14x(e^(1/x))−14x limit x approaches infinity using lhospitals rule

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Q: Find a nonzero value for the constant k that makes th tan(kx) x 0 Continuous at x = 0.

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Q: Find the limits sin(3t) lim In(sin(3t)) i+ In(tan(4t))" j+tln(3t) A t→0 sin(4t)

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Q: Find the linearization of ƒ(x) = sqrt(x + 1) + sin x at x = 0. How is it related to the individual…

A: To determine the linearization of the function at x=0.

Q: Let sin(r-y) ||| + \y| +0 (x, y) = (0, 0) f(x, y) Is f continues at the origin? Why?

A: Solved below

Q: At which points does f(x) = 2 sin x - cos 2x have an absolute maximum value and what is the maximum…

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Q: dy at x = 2. dx 2 10. Given the curve y= 5 - (x-2)³, find (A) 3 -- (B) 3/2 (C) 5 (D) The limit does…

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Q: I* cos z lim 1³+2

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Q: The linear approximation at x = 0 to sin(6x) is A + Bx where A is: Preview and where B is: Preview

A: First of all, consider the formula to find the linear approximation at any point a for function any…

Q: 1. If y= tanx, prove that y"=2(y² +1)(3y² +1).

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Q: Express the limit as a definite integral on the given interval. lim [9(x;)³ – 9x;14x, [2, 8] i = 1…

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Q: Find fyxyx for f(x, y) = ln(xy) − cos (xy) at (1, π)

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Q: Use a linear approximation of f(x)=cos(x) at x=5π/4 to approximate cos(222∘)

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Q: Find t6e eavation of tangent ine of fcx) = X+) at X=2 X-3

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Q: Prove that for all x € [1, 00), – sinh (- |cosh'(x)|) = V -1. %3D Ouest!

A: Proving of function  sinh(cos-1(x))

Q: (a) Evaluate the integral t tanx dx by using the reduction formula of tangent function.

A:

Domain

In simple mathematics terms, a domain is defined as the space on which all the possible inputs for the function will lie. It can also be expressed as a set of departures for the required function.