9. 6. If sin(0) = 41 and tan(0) = find sec(0). 40 %3D |

Q: Graph the function defined as follows over a two-period interval. y = 2 cos x

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Q: 6) Find all relative extrema in the function h(x)=cos on the interval [0, 2].

A: For any function f(x) which is defined over an interval [a,b], its relative extrema values are the…

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Q: 10 Use aepropriate substitution Ond then a trigonometric oubtitution to evaleiate the integial. dx…

A: This question can be solved using the concept of integration by substitution.

Q: 11. Determine the values of n and h required to approximate e2r sin 3x dx to within 10-4. Use a.…

A: I am attaching image so that you understand each and every step.

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A: Since you have asked multiple question, we will solve the first question for you as per our guide…

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Q: Which of the following is correct? " 17 3 (3 sinh-(x)) = (coth"(x) = (지 < 1) V - 1 dx Option 1…

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Q: 10. Suggest ways to avoid loss of significance in these calculations. (1) Vx² +1-x; (3) sin x- tan…

A: 1 x2+1-x By rationalization  =x2+1-xx2+1+xx2+1+x=x2+1-x2x2+1+x=1x2+1+x Therefore, as x→+∞ there…

Q: Find the length of the curve over the given interval. r = 6 – 6 sin(0) on the interval 0 < 0 s 2n

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Q: B: 3:Use Gamma & Beta properties to evaluate : f (In x) 3 dx

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Q: A ( sinh x- coshx tanh e 6)

A: You all need to have the idea of hyperbolic and their basic calculus.

Q: 12) * 1 Differentiate y =sinh

A: Given:y=sinh212x

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A: According to question,Given function,y = sin x -2,where,0o ≤ x ≤ 180o,

Q: 1. The air in a certain room 150 x 50' x 12' tested 0.2% CO2. Fresh air containing 0.05% CO2 was…

A: Solved below

Q: 7 5 5. sec '(In t) tan° (In t) dt t

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Q: / (3cosh m 2 cosh m sinh mdm +e°

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Q: 2) Give a big-Oh estimate, O(x³), for the function f(x) = (1 + 2x + 2cosx + 2r*)(log x² + 3lx| + sin…

A: 2 Given function is fx=1+2x+2cosx+2x2logx2+3x+sinx+cosx. We have to estimate Ox3 and determine the…

Q: 6) Using gamma function, evaluate So 6 хе 2x dx

A: Introduction: Gamma function is an integral function that is defined through an integration. The…

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Q: S cos ( x^3 ) dx = * sin ( x^3) + c 3x^2 sin (x^3 ) + c - sin (x^3 ) + c - 3x^2 sin ( x^3) + c none…

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Q: QUESTION 3 a) Evaluate the integral tanh (2x)sech (2x)dx.

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Q: Graph the function defined as follows over a two-period interval.

A: It is given that,  y=-12cos x It is known that general equation for such functions is given as,…

Q: 4) u = x² sin=1 x 5) Ø = tan¬1 3 0 6) y = In(7 – 3x)

A: This question is taken from the derivative in which we have to find the derivatives of the given…

Q: B) If sinh 0 V3 Find cosh 0, tanh 0, coth 0.

A: Given: sinhθ=32 To find: coshθ, tanhθ, cothθ. Solution: We have identity, cosh2θ-sinh2θ=1 Putting…

Q: 8. Using any work found in Question 7, determine the 3x (x? - 5)° dx a.

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Q: 2 1 e. Use your answers for parts c and d to estimate -dx using Simpson’s rule with n=8 1+x

A: We have to find the integral by Simpson rule

Q: 1.Find dy/dx of the following: 5. y = Incose* tan x 6. y = ln(1-xe) 7. y=eta et 4. y= In x 8.…

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Q: 12. Find the derivatives (1st of the ff. function or as specified in the problem. Simplify the…

A: Since you have asked multiple questions in a single request so we will be answering only first…

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Q: 4 cos (2x e function f is defined by f (x) values of x on the interval (0, 3 such that the line…

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Q: 8. Suppose that the tangent line to the graph of ƒ(x) = r0) at r = 1 is equal to the tangent line to…

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Q: 26. If cosh 2z = ° then the positive valuc of sinh 2r is 4 B D com

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Q: 5) Give a big-Oh estimate, 0(x³), for the function f(x) = (1+ 2x + 2cos x + 2x2)(log x² + 3|x| + sin…

A: 5 Given that the function is fx=1+2x+2cosx+2x2logx2+3x+sinx+cosx......1. We have to estimate Ox3 and…

Q: S₂ 10 x 4x²8x +9 in14 (x-1)² +51 + √5 tan¹ (²²) + C Option 1 In 14 (x-1)² +51 + √5 tan¹ (2x = ²2) +…

A: SOLUTION-

Q: 4. Find the exact values for each of the following. а. sec-1 b. sec-(-V2)

A: The detailed explanation and answer is given below:

Q: 2/solve the differentialequation by using methad af Variation of (complete salution is vequired)…

A: Given equation is y'''+9y'=1cos11x               (i) Let us consider y'=z. Then, eq. (i) is reduced…

Q: 3 2 10) Find the arc length of f(x) = x3 + 10 On [0,8].

A: To find the length of the arc for the given function f(x)=32x23+10 on the interval [0, 8]

Q: 7. Over the domain 0s x s2n, the equation cos(x)-sin(x)%3D2 cos(2x) has:

A: We find the solution in the following way by using trig identities.

Q: d. Show that sin ž is exists or not? e. Verify that the derivatives of sinh z. f. Solve the value of…

A: The solution are next step

Q: Question 7: Use the trapezoidal rule with 6 intervals to evaluate f* 10 x7 dx ,giving the answer…

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Q: 1) fcoe cos x sin rdr

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Q: 2 Recall thal cos-x= arccos x, Find /2 X Sin (cos x) dx. C.

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Q: y= 13.cos(5x) + sin (5x) 04 X6 2 COS 1.) Local Maximum poin to) are ? 2) Local Minimum. point(s) are

A: Maxima and minima occurs at dydx=0 We also check value of d2ydx2 to clarify that point is minima,…

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Q: 8. [Calculator Active] Find the least integer value n, such that T,(x)=1-+-++(-1)" - successfully…

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Q: Given that ſ♫ sin xdx = 2, find the average value of the sine function on the interval [0, π]. Also,…

A: Please see the below picture for detailed solution .

Optimization

Optimization comes from the same root as "optimal". "Optimal" means the highest. When you do the optimization process, that is when you are "making it best" to maximize everything and to achieve optimal results, a set of parameters is the base for the selection of the best element for a given system.

Integration

Integration means to sum the things. In mathematics, it is the branch of Calculus which is used to find the area under the curve. The operation subtraction is the inverse of addition, division is the inverse of multiplication. In the same way, integration and differentiation are inverse operators. Differential equations give a relation between a function and its derivative.

Application of Integration

In mathematics, the process of integration is used to compute complex area related problems. With the application of integration, solving area related problems, whether they are a curve, or a curve between lines, can be done easily.

Volume

In mathematics, we describe the term volume as a quantity that can express the total space that an object occupies at any point in time. Usually, volumes can only be calculated for 3-dimensional objects. By 3-dimensional or 3D objects, we mean objects that have length, breadth, and height (or depth).

Area

Area refers to the amount of space a figure encloses and the number of square units that cover a shape. It is two-dimensional and is measured in square units.