. Proof of (cos x) = - sin x Use the definition of t dx and the trigonometric identity cos(x + h) = cos x cos h sin x sin h to prove that (cos x) dx = -sin x.

Q: Eliminate the parameter t from the following. x = sin t − 5, y = cos t − 4

A: Eliminate the parameter and simplify it.

Q: Determine the value of f(z) = e*cos y+ ie*sin y at z = In 4+ Ti/6

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Q: (a) Find dy/dx for 3 tan x – In x x2 (b) Find f"(x) for the following function: e" In(x**) f(x) = x…

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Q: Determine the value of f(z)=e*cos y+ ie*sin y at z = In 4+ Ti/6.

A: For a complex number, z=x+iy , x is the real part and y is the imaginary part .

Q: 3 7 cos z Evaluate the definite integral: dæ sin x 6.

A: Evaluate the Definite Integral : ∫π6π37cosxsinxdx

Q: If f(z) = 2 sin I +3 cos z, then f'(x) = %3D

A:

Q: 5. Assuming that (d/dx) (sin x) = cos x and (d/dx) (cos x) = - sin x, prove each of the following. d…

A: The quotient rule of differentiation states that uv'=u'v-v'uv2. (a) Write cot x=cos xsin x and use…

Q: Find cos (z+2) dx. O-sin (x + 2) +C O sin (x4 + 2) +C O sin (x* + 2) +C sin (2* +2) +C

A: Let's find.

Q: Let  f(x) = cx + ln(cos(x)).  For what value of c is f'(pi/4)=4

A: sol:-    Given f(x) = (x+ln(cosx)  differentiating ω. r.t   x, we get    f1(x) = c+1cosx(-sin x)…

Q: [et Suppose A(t) =0 0. cos t sin t, show that A(t)-1 exists and then find it. - sin t Co t. -

A: Given- At = et000cos tsin t0-sin tcos t To Show- Show that At-1 exists and then find it.

Q: 2. Find the domain of the function. cos x b. f(x) = 1 - sin x

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Q: 1+cos 0 + sin 0 sin 0 Prove = 2 csc e 1+cos e

A: To prove : sinθ1+cosθ+1+cosθsinθ=2cscθ

Q: x sin (x²) cos(x²), from a = 0 to b = x 2

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Q: Which of the following may be solved by a direct application of L'Hopital's rule? sin 2x lim x→0-…

A: We have to check

Q: 2 Find the maximum and minimum values for f(x) = . Determine the -4 + cos x+ V3 sin x angles at…

A: Consider the  given function fx=2-4+cos x+3  sin x The value of the function at the endpoints of the…

Q: #2. Verify Clairaut's Theorem for the given function f (s, t)= In (st)-s* sin (6t) +st.

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Q: what functions are odd, even, or neither odd or even   (d) f(x) = 5cos(x) is______ (e) f(x) =…

A: A function f(x) is, i. even if f(-x) = f(x), for all values of x ii. odd if f(-x) = -f(x), for all…

Q: Find the root of f(x) = e −x (3.2 sin(x) − 0.5 cos(x)) on the interval [3, 4] up to 1 d.p.

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

Q: Consider the function Vx² sin? COS X - X f(x) = Vx-1 sin ++1 Determine f'(0.25) using 3 point…

A: In this question, we need to determine f'(0.25)  using 3 point central difference with h=0.01.…

Q: if y = a sin x Prove a +b CosX a cos + b %3D 2 (atb cosx) 11

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Q: 4. Use the inequality | sin r|< |x| for x E R to show that the sine function is continuous at r = 0.…

A: Sine function and it's continuity at 0

Q: 13. For J* sin x dx, what is u? sin x dx 2x dx -x cos x+ 2x sin x+2 cos x +C Oc. OD.

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Q: For what values of x does g (x)= x – sin x have a horizontal tangent line? Consider values of x in…

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Q: Sketch the following between x = 0 and x = 4 pi      y =  sin x + cos 2 x

A: Given: The function is  y =  sin x + cos 2 x

Q: The "equation cos x "y sin x is A Iny In (cos x) + k B Iny = In (sin x) + * c. Iny=-In(sin x) + k…

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Q: Show that COS x dx a² – x² sin a 2а where a is some positive number.

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Q: calculate SN given by Simpson’s Rule for the value of N indicated.

A: Given, ∫01cos(x2)dx  and N = 6 Solution: Simpson's rule: Area = ∫abf(x)…

Q: (1) (sinz) + (cosr)* sin x COS x (2) tan x in terms of sin x, cos x %3D d. d. ( sin x COS X %3D dx…

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Q: 1+e² sin z + z cos z

A: Introduction :

Q: tan? z sec? x + sec a Prove 1-cos I

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Q: a. Use the definition of the derivative and the identity sin(a + B) = sin(a) cos(B) + cos(a) sin(B)…

A: As per Bartleby guidelines, for more than one questions asked, only one is to be answered. Please…

Q: 25. Assuming that (d/dx) (sin x) = cos x and (d/dx) (cos x) = - sin x, prove each of the following.…

A: Our Aim is to prove the derivative of the following:-(i) ddxtan (x)=sec2 (x)Proof⇒ddxsin (x)cos…

Q: S sin x In(cos x) dx

A:

Q: 7) Determine an eq ,in (x) and (y) , and then find a) y sec 1t , x csc-1t b) y = (sin 0)* ,x = (cos…

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Q: If y = sin (sin x) and d dy tan x + f(x)= 0, then f(x) equals dx2 (A) sin² x sin (cos x) (C) cos? x…

A: Introduction :

Q: Which of the following is correct? e* dx = e* + C Ssine sin(x²) dx cos(x²) + C 2x dx = In(x³) + C…

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Q: Given: y = sinh(ln(cos a)); Find y'. O (E) None of these O tan(x) sinh(In(cos x)) O sinh(ln(cos r))…

A: Given y=sinhlncosx To find y':

Q: - Using Euler's equation, show that- : z fain (K 0)} - z sin Ø z2 – 2zCos Ø +1

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Q: Evaluate (cos x)(n sin x)dx. А In V sin x + C В sin x (1 – In sin x) + C C sin x (1 + In sin x) + C…

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Q: e* (1 + sin x de. nx] Evaluate 1 + cos x

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

Q: 2Tt Prove that a" sinax cos bx dx = 0 0.

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Q: a Show that (sin(m + n)x + sin(m – n)x) b Hence, without using the product rule, differentiate sin…

A: We will find out the required values.

Q: When J x°cos (x-)dx is evaluated using IBP, the value of J v du is? A - cos (x2) B none of the…

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Q: 1 The function (x) = x sin x satisfies the following equation: f"(x) + f(x) + t cosx = 0. The value…

A: solve the differential equation

Q: 2- Exercise: Evaluate a) L{4x? – 3 cos(2x) +5e*} b) L{4+sin (x) – e**}

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Q: (d) Using your answer to part (c) compute h'" (x) where h(æ) = 1/ cos(x) and a is such that cos(æ) #…

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Q: Prove that d/dx [cos x] = −sin x.

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Q: b. Determine real (e/z) in terms of x and y. C. Use Euler's formula to prove that expression; = cos…

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Q: Mclopens serial f(x) = cos x she ?

A: Given function is f(x)=cosx

Rate of Change

The relation between two quantities which displays how much greater one quantity is than another is called ratio.

Slope

The change in the vertical distances is known as the rise and the change in the horizontal distances is known as the run. So, the rise divided by run is nothing but a slope value. It is calculated with simple algebraic equations as: