Suppose that f(x) = 0.5 cos x for -T/2 -"/4) %3D e. Determine x such that P(X < x) = 0.95

Q: Compute cosh x and tanh x, assuming that sinh x = 0.8.

A: Here given as sinhx=0.8 Use the identity…

Q: Find the exact value. In 3 0 ³ sech 4 x tanh x dx

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Q: Consider the function f(x) = cos x − 3x + 1. Since ƒ (0)ƒ () < 0, f(x) has a root in [0]. If we use…

A: For finding a zero of a function f, the secant method is defined by the recurrence relation.…

Q: 8. Find the principal value of Arc tanh(1 + j2)

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Q: Use Secant method with p, =1, p =1.2 to find the root of f(x)= ln x – cos x that is accurate to…

A: Solution:Let f(x)=log(x)-cos(x)a=1, b=1.2, f(a)=-0.5403, f(b)=-0.2832Here f(a)&lt;0 and f(b)&lt;0.…

Q: Use forward and backward difference approximations of O(h), and a centered difference approximation…

A: Given function is, fx=sinx1+cos Then the forward Oh is,…

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: Use Simpson's rule with n = 4 to approximate cos(x) dx 1

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Q: Use the trapezoidal rule withn = 4 to approximate 5 cos(x) -dx- Keep at least 2 decimal places…

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Q: cos x 13. lim x→(T/2)* 1 – sin x

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Q: Consider the function f(x) = cos x − 3x + 1. Since ƒ (0)ƒ (=) < 0, ƒ (x) has a root in [o,]. If we…

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Q: 2. Compute for a real root of 2 cos x- sin Vx 1. 4. accurate to 4 significant figures using…

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Q: .Find a reduction formula for ea* sin" x dx. Hence evaluate e* sin x dx. 3

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Q: 2. Given: cosh x==(e²+ e*), sinh x=(e-e), use these 1-1/1 definitions to show that cosh’x−sinh’x=1.

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Q: hich the extrema occur. g(x)=x^2+cos⁡(x^2 ) on [-√π,√π]

A: The function given is gx=x2+cosx2 on the interval [-√π,√π]. To find the extrema of the function…

Q: 10 Use Simpson's Rule with n = 8 to approximate f cosx dx. 2

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Q: If f(x) Files = Time left 0:5 sin²x and g(x) = 1 + cos²x, how are f'(x) and g'(x) related? Maximum…

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Q: Find that antiderivative of tan° x whose value at x = 0 is 1. O is

A: Given that: tan3x

Q: Use differentials to estimate sin(0.1). A) 0.0017 0.0099998 0.0998 D. 0.1

A: Give: To using differential s to estimate value of Sin(0.1)

Q: 31. Verify the formulas sinh-x = In |x + Vx² + 1| coshx = In |x +Vx² – 1| (for x > 1)

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Q: Find y' if y= In(tanhx) +cosh-(coth2x) Select one: O y' = cothx- 2csch2x 1 O y = -2csch2x sinh x…

A: The differential of products of trigonometric functions can be calculated using the product rule.…

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: (ii) Show that 1 d (tanh-1 x) = dx 1- x2 Hence, or otherwise, show that, 27 tanh-1x dx =- In 4 2. 1…

A: Evaluate: and

Q: Consider the function f(x) = cos x - 3x + 1. Since f (0)ƒ () <0. f(x) has a root [] If we use secant…

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Q: Find an approximate solution, accurate to 5 decimal places, to the equation cosx=x2 that lies in the…

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Q: What is the derivative of y = 10sin 5x 5 In 10 cos x 10in 5x 5 In10 (10sin Sx) A. C. 5 cos x In 10…

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Q: Consider the function f(x) = cos x − 3x + 1. Since f (0)f () <0. f(x) has a root in [0]. If we use…

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Q: Suppose that the tangent line to the graph of f(x) = x(6*) at r = 1 is equal to the tangent line to…

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Q: If f(x)-logCos4x + sinx.Then find 9 (x) JP at x= sec 2c dx 6.

A: Given function is: f(x)=logsec2x|cos4x|+|sinx| To find the value of 9df(x)dx at x=-π6

Q: Find dy for X=3sec-vE tan (2t) and

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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: The approximation of the root x* of the function f(x) = -x + sinx-1 accurate to within 10-3 using…

A: Needs 2 iterations

Q: Consider the function f(x) = cos x − 3x + 1. Since ƒ (0)ƒf () < 0. f(x) has a root in [0]. If we use…

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Q: Which is the derivative of y= sin In(5x +2)? * 5 cos In(5x + 2) In 5 5Cos In (5x+2) 5x+2 O Option 3…

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Q: Evaluate the definite integral.

A: ∫012arccosx1-x2 dx Consider, ∫arccosx1-x2 dx Now put, arccosx=t⇒-11-x2=dtdx⇒11-x2 dx=-dt Therefore,…

Q: Find the extreme value/s of f(x) = 4 sin² x − cos 2x on . (³347) 3π 5π 2' 2

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Q: Q2): If sinh(x) =find tanh(4x). %3D

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Q: E PARTICULAR SOLUTION OF EVERY EQUATION GIVEN. [tan y – (In x)°]dx = 0 When:x = 1; y = " 4

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Q: 8. (a) Evaluate the indefinite integral dx sinhx+coshx e 4x (b) Find and simplify the derivative of…

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Q: Consider the function f(x) = cos x − 3x + 1. Since ƒ (0)ƒ () <0, f(x) has a root in [0]. If we use…

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Q: Use Simpson's 1/3 rule with (n₁ = 2), and Simpson's 3/8 rule with (n₂ = 3) to estimate tan-¹(2).…

A: We have to estimate the given function.

Q: 4. Use Secant method with p =1, p =1.2 to find the root of f(x)= Inx – cosx that is accurate to…

A: Given, fx=ln x-cos x; p0=1; p1=1.2; As it is known that the secant method is given as,…

Q: Compute for a real root of 1 2 cos Vx – sin vx = accurate to 4 | 4 significant figures using…

A: 2cos(33)-sinx=14;   x0=π f(x)=2cos(33)-sinx-14 f(x)=0 ⇒2cos(33)-sinx-14=0 x=cos-11214+sinx3=ϕ(x);…

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

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Q: The approximation of the root x* of the function f(x) = ln(x + 1) - x + 3 accurate to within 10-2…

A: Introduction: Another recursive technique for approximating the polynomials' roots is the secant…

Q: Find y' of y= In(tanh2x)

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Q: What is the derivative of y = 10sin Sx 5 In 10 cos x 10sin Sx 5 In10 (10sin Sx ) A. В. C. 5 cos x In…

A: Given: y=10sin 5x To Find: The derivative of the given function.

Q: - In-2. Hence show that In = 01 tan" x dx = n - 1

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Q: If f(x) = 4 cos x – 6x, find the relative percentage error in f(x) for x=0, if the error in x is…

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Q: a(cos2x) sin(x-) TC 1. f(x) = tanx 4. What values should a and b take for the function fx) to be…

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