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

A: Here is the solution:

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: 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: 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