Example 7: Find lim sin(a+h)-sin in a h→0 h Solution // lim h→0 sin(a) cos(h) + cos(a) sin(h) – sin(a), h lim( h→0 lim h→0 sin(a) ((cos(h) − 1) + cos(a) sin(h) lim h→0 -sin(a) (1 - cos(h) + cos(a) sin(h) h -sin(a) (1 - cos(h) h + lim( h→0 sin(h) cos(a) h = cos a

Q: 3x+7 sin2x x+x.cosx 1- lim- x2-2 lim 2x2+x 3 - lim- x→0 2 - 00+X x→0 sinx.cosx 1 lim x-1- 1-x2 x-3…

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Q: f(x) = { cos x, xpi  which lim does not exist

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Q: For (cos(2x) – sin cos(x) – sin(x) - sin(2x) cos (2x)) +C. What is F (x)? A sin cos³ (x) – cos(x)…

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Q: If f(x) = tan (3x), then f'(x) = (A) 12 tan (3x) sec?(3x) (B) 4 tan (3æ) sec2(3x) (C) 12 tan (3x)…

A: derivative

Q: X – sinx (i) lim x2 d (ii) ( e2x · cos x) dx (iii) J tan 2x dx d (iv) dx ( sech 2x) 1 (v) -) dx S(…

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Q: 10. | [3 - e-lxl – cos x + log(x²)]dx = 0 x³ +4x – sin x 11. x² – 7 -dx 3 0

A: 10. ∫a53-e-x-cosx+lnx2dxEliminate absolutes =∫a53-e-x-cosx+lnx2dxApply the Sum Rule:…

Q: If f (x) = 1 and (a, ƒ(a)) and (a + h, f(a+h)) are points on f(x), where h = 0, then 2x -1 f'(a) =…

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Q: Find where z = sin (x²) cos (y) COS © 6.x sin (x²) cos (y²) COS 2.x sin (2²) 2x cos 2.x sin (x²) cos…

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Q: (sinx -) tan*(5x) Q3/ 1)- lim, 2)- limx-0 (3sin?x -sinx +1) x sin3 (2x)

A: There are multiple question. As per Bartleby policy Kindly ask other question separately.  Given…

Q: Let G(z)- sec 0 de for z in [0, 1]. Find G" (z).

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Q: cos(x) sin (2x) lim x X sin(x) – 1

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Q: Solve sin (x) + sin(x) = 0 on [0, 27]

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Q: Let f(x) (8 sin x + 3 cos æ)tan-x f'(x) =

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Q: 1 If g(x) = [** sec(t³) dt, then g'(x) = x O-3x² sec(x³) – sec(x³) — sec(1) tan(1) + sec(x³) tan(x³)…

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Q: Evaluate / 3 x sin(x)dx 03 (sin(x) – x cos(x)) + c Osin(x) – x cos(x) + c 03 x sin(x) + 3 cos(x) + c…

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Q: Cos(x) 一+Sin (x) sec (x} I +sin (x) Cos(x)

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Q: Solve (tan(z) - 1) (3 tan(x) +√3) o over the interval (-∞, ∞).

A: Here is the solution:

Q: Evaluate / 11 x cos(x)dx O11 sin(x) + 11 x cos(x) + c Oc – 11 (x sin(x) + cos(x)) Ox sin(x) – 11…

A: Topic- Integration

Q: A power signal which is periodic with period 2n and is characterized by the form f(x) Expand f(x) in…

A: Given, fx=sinhxcosx, -π≤x≤π Since, f is periodic of period 2π then, fx+2π=fx Then,…

Q: sin(cos x) limx-n/2

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Q: If g(x) = 3 sin x + 2 cos x + 5, then g' (3) = A B 12/3-√3 - 3/2+√3

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Q: 1 sin(x) (D²+1)³

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Q: integrate (sin(x)*tan(x)-cos(x))/tan (x+1)

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Q: sin(3t) i+ In(tan(6t)) -j+(t – 2) cos(3t) k , find lim F(t). t+0+ Let F(t) sin(6t) In(sin(3t))

A: solve the following

Q: If f(x) = (x² – 1) (sin (x)) , what is f'(x)? O f '(x) = (x² – 1) cos (x) + sin(x) (2æ) O f (æ) =…

A: Consider the given function: fx=x2-1sinx Product rule of differentiation is given by:…

Q: [(2tan(x)/1+sec(x))+(2+2sec(x)/tan(x))]=4csc(x)

A: Consider the left hand side,

Q: Find the function f(a) such that f'(x) = 5 sinh(x) – 2 and f(0) = 4. a) O f(x) =-5 cosh(x) – 2 z - 1…

A: Given that f'(x)=5sinh(x)-2 and f(0)=4 To find the function f(x)

Q: e*sin³ (=) e*sin³ 3 (t 3 x23 sech (x-2) xº sech (x-2) F (x) = S f(x), if x 2

A: Given that  gx=exsin3πxx2sechx-23if x≤20if x>2 Find the left hand limit of the function at x=2.…

Q: Ssin(x)cos(2x)sin(3x) dx sin(3x)cos(3x), sin(2x)cos(2x) , sin(2x) + + C 12 8 8. 4 sin(6x) sin(2 x),…

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Q: cos (x + h) – cos x f'(x) = lim h0 57. h cos x cos h – sin x sin h – cos x lim h sin h cos h = lim (…

A: Given: f'x=limh→0cosx+h-cosxh

Q: (a) [In(4) - 2e¹³] dx d b) dx d (c) [2²² - 1 (2²)] = 4e³x In(x [sec (12r) + tan-¹(2x)]

A: NOTE: Refresh your page if you can't see any equations. .

Q: If f (x) = - cos(x), then f (0)(x) is equal to A - sin(x) B - cos(x) В © sin(x) D cos(x)

A: We have to differentiate the given function 9 times

Q: Ssin(x)cos(2x)sin(3x) dx O sin(6x) sin(2x) , sin(2x)cos(4x) 24 8 8 + 4 sin(3x)cos(3x), sin(2x) +…

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Q: The derivative of f(t) = sin(a* + 2 a+ 22 - a) is O f(a) = (4 a+6 a² + 4 * – 1) cos(a*+2 a³ + 2 #² –…

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