103. GU Plot the graph of f(x) sin mx sin nx on [0, 7] for the pairs (m, n) = (2, 4), (3, 5) and in each case guess the value of I = | f(x)dx. Experiment with a few more values (including two cases with m = n) and formulate a conjecture for when I is zero.

Q: 9. cosh x + sinh x= e* %3D

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Q: a) By using the graph of function y = cos x, graph the function y =- cos (3x +) x-8

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

Q: 9. cosh x + sinh x = e* %3D

A: To Prove,                cosh x+sinh x=ex

Q: nd all values of x in the interval [0, 2x] that satisfy the equation. (Enter your an 9 sin(2x) = 9…

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Q: 1) Match each function with its gray-Cos Cos x y = Sin x y=-Sin x y =-Cos x Slide correct function…

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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: nx and y=cosx from x=- to x=- 4 4

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Q: 1 9. In the proof that (sin-1x) = that sin(sin-1 x) = x. It is also true that sin-(sinx) = x; could…

A: Differentiation of function gives the change of function with respect any variable. The inverse…

Q: 17. Why doesn't the definite integral 1-x² dx make sense? (Hint: Think about domains.)

A: To find: The reason why the definite integral ∫231-x2dx does not make sense. Explanation: Substitute…

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

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

Q: 3 9) Use y'(3) to determine if the graph of y = 4 cos x +- is increasing or decreasing when x = 3.…

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Q: undetermint coedticients 11 ON-4y = G²-3) sin x

A: The given problem is to solve the given non homogeneous differential equation using method of…

Q: sin 2n x Prove that: dx = 0 for all n e N. sin x

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Q: 57 6. Find an equation of the tangent line to y = f(x) = cos²(x) at %3D

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Q: 6. Suppose you wish to differentiate g(x) = sin²(x)+cos²(x). What is the fastest way to do this, and…

A: Given,

Q: 1) If y = (x-a)√2ax-x² + + a is constant. x- -1(*-ª) ,then y' = 2√2ax - x² a² sin-¹ a²

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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: Q3: Let cosh(x)3D5, x>0 , Find values of: sinh(x), tanh(x).coth x ,sech x,csch x

A: Given, cosh(x)=5, x>0

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

A: To Determine: What value of x does the graph meet the x-axis. Given function is :…

Q: Evaluate 1 ei sin x cosx dx using Simpson rule with h = 20

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Q: Estimate the error if P3(x) = x - (x3>6) is used to estimate the value of sin x at x = 0.1.

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Q: Apply Newton's Method to f(x) and initial guess xo to calculate x₁, x2, X3- f(x) = 1 – 5x sin(x), xo…

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Q: Find the absolute extrema of the function on the closed interval. y = 9 cos x,    [0, 2?]

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Q: 2 Find the x-intercepts of y = 2 sin x + sin x – 1 on the interval [0, 27). %3D

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Q: (2) If y = (sin-1(x))², prove that (1- x2)y" – xy' - 2 = 0.

A: here first we will derivative with respect to x then squaring both side and put value of the y then…

Q: 9. Solve tan x for x where 0<x<90* V3 Enter your next step here

A: Just observe that its value of tan(30°).

Q: b. Express tanh x in terms of e* and e-* and hence show that 2 tanh x tanh 2x = 1+ tanh? x' c. Given…

A: (b) To proof :   tanh2x=2tanhx1+tanh2x It is known that, sinhx=ex-e-x2coshx=ex+e-x2 so,…

Q: Find the root of f(n) = 3x - cos(x) -1 = 0

A: Please rate and feel free to ask any query about any part.

Q: 57. Extension of Example 8 Show that cos (x) is dx sin (x). 180

A: The objective is to show that ddxcosx° is -π180sinx°. The function cosx° is given in degrees bu the…

Q: Q3: Find value of x if 3 cosh x- sinh x= 4

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Q: 6. Approximate the real root of x – cosx = 0 to three decimal places. Let xo = 0.8 and find x1, x2,…

A: Let f(x) = x - cos(x) x0 = 0.8 By using the Newton-Raphson method to approximate the root,…

Q: 6. Evaluate |2 Sin xʻdx, by (i) mid-point rule, and (ii) Simpson's 1/3 rule.

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Q: 55. f(x) = x² + cos ¹x on [-1, 1]

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Q: 5. Evaluate | (x² +1)* dx using trigonometric substitution as your first step (not a u-sub as your…

A: The solution is given below in the next step:

Q: 4. Find the absolute maximum and minimum values of the function f(x) = cos²x-3 sinx on the interval…

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Q: 13 20 Find for Two only of the following: dx 1- y=xtanhx 2- y =cosh 3x- sinh²3x

A: We have to find derivative

Q: 3. Use Simpson's rule to calculate x² sin x dx to within 2 × 10-5 of the exact value.

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Q: 47. Let y = sec-x. Show that tan y = vx? – 1 if x > 1 and that tan y = -Vx? – 1 if x 0 on (0, 3)…

A: Consider the function of x and solve further-

Q: 4. Evaluate if they exist: (a) sinh x dx (b) lim , sinh x dx r+00

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Q: 9. Prove that | sin n0/sin 0| <n, limiting values being used when sin e = 0.

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Q: dy/dx for (ln(tan(2x)-sqrt(3+e^2x) / (pi(x)^3-cos^2(-5x))

A: Given,     y  =  ln(tan2x)-3+e2xπx3-cos2(-5x)

Q: Cos x dx In x (sin x) () - dæ. (In x)²

A: We have to find the value of the integral : ∫cos(x)ln(x)dx-∫sin(x)1xln(x)2dx

Q: 52. Verify that f(x) sin x is an odd function and u fact to show that '3 sin x dx < 1 -2

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Q: 2. Consider finding the root of f(x) = e"(3.2 sin(x) - 0.5 cos(x)) on the interval [3, 4], this time…

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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: 5. Find the PARTICULAR SOLUTION: y' = 1+ 3y tan x when x = 0 ; y = 1

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Q: 2. Is it possible to write sin (37x) as a linear combination of sin(2rx) and sin(Tx) for all values…

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