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determine wether or not the function f,where f(x) = { ((2x + 1, 0≤ x <2)),((7−x, 2 ≤ x < 4)),((((3x)/4) , 4 ≤ x < 6)) :} is continuous in the interval [0,6[ |
f : x → { ((1 + x, if x<1)),((2x−1,if x>1)) :} investigate the existence and non existence of the limit of f at the point x =1 |
let f(x) = ((tanx)/(tan2x)) . Find the points of discontinuity of f on [0,2π] and determine wether each duscontinuity is a point discontinuity,a jump discontinuity,or a vertical asymtote |
Determine the value of a and b fir which the function f,defined by f(x) = { ((−2sinx, x < −(π/2))),((asinx + b,−(π/2) ≤ x < (π/2))),((cosx, x > (π/2))) :} is continouos |
show that f(x) = ∣x∣ is not differentiable at x=0, where ∣x∣ denotes he absolute value function |
investigate the continuity of f ,given by f: x → { ((1−x, if x<1)),((0,if x =1)),((x^2 −3x + 2,if x >1)) :} at the point x =1 |
find the value of λ for which f : x → { ((2λ − x, if x < 1)),((λ^2 + x −1, if x > 1)) :} has a limit as x→ 1 |
prove that (1−itanθ)/(i+cotθ)=itanθ pleas sir help me? |
find a) Lim_(x→−∞) ((ln(1+e^x ))/e^x ) b) lim_(x→+∞) ((√(x^2 + 3x)) −x) c) lim_(x→0) (√x) ln(sinx) d) lim_(x→+∞) ((e^(2x+1) −e^x )/(x^2 −x−1)) e) lim_(x→−∞) [(√(1−xe^x )) ] |
give: a,b,c>0 if a∣b and b∣c prove : a∣c |
evaluate Lim_(x→+∞) xln (((x+1)/x)) |
how many divisors does 38500 have? |
solve 87x ≡ 3 (mod 5) and 55x ≡ 35 (mod 75) |
evaluate ∫lnx dx |
expressf(θ)= 8cosθ −15sinθ in the form rcos(θ + α), where r>0 and α is a positive acute angle hence find the general solution of the equation 80cos θ −150sinθ = 13 the maximum and minimum value of (5/(f(θ) + 3)) |
Given that the function f(x)= x^3 is differentiable in the interval (−2,2), Use the mean value theorem to find the value of x for which the tangent to the curve is parallel to the chord through the point (−2,8) and (2,8) |
find the general solution of sin4x + cos2x = 0 |
prove by induction that 4^n + 3^n +2 is a multiple of 3 ∀ n Z^+ |
prove that they are infinitely many primes |
given the 3^(rd) degree polynomial P(x) = (2x −1)(x−3)Q(x) + 12x−8 given that (x−1) is a factor of P(x) and P(0) = 10 find Q(x) |
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prove that : 2^π >8 |
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Pg 1321 Pg 1322 Pg 1323 Pg 1324 Pg 1325 Pg 1326 Pg 1327 Pg 1328 Pg 1329 Pg 1330 |