লিমিট
Let fff be differentiable (xϵR)(x\epsilon R)(xϵR), if f(2)=−2f(2) = -2f(2)=−2 and f′(x)≥2f'(x) \geq 2f′(x)≥2 for xϵ[1,6]x\epsilon [1, 6]xϵ[1,6], then-
f(6)<6f(6) < 6f(6)<6
f(6)≥6f(6) \geq 6f(6)≥6
f(6)=5f(6) = 5f(6)=5
f(6)≤5f(6) \leq 5f(6)≤5
By LMVT there is c∈(1,6) c \in(1,6) c∈(1,6)
Such that f(6)−f(1)6−1=f′(3) \frac{f(6)-f(1)}{6-1}=f^{\prime}(3) 6−1f(6)−f(1)=f′(3)
f(6)+25=f′(3)f(6)=5f′(3)−2≥5.2−2f(6)⩾8=>f(6)≥6 \begin{array}{l} \frac{f(6)+2}{5}=f^{\prime}(3) \\ f(6)=5 f^{\prime}(3)-2 \geq 5.2-2 \\ f(6) \geqslant 8=>f(6) \geq 6 \end{array} 5f(6)+2=f′(3)f(6)=5f′(3)−2≥5.2−2f(6)⩾8=>f(6)≥6
এর সঠিক মান কোনটি?
0. limx→0(1+5x)13x \lim_{x \to 0} \left ( 1 + 5 x \right )^{\frac{1}{3 x}} limx→0(1+5x)3x1 এর মান নিচের কোনটি ?
limx→0(1−cos2x)sin5xx2sin3x=?\displaystyle\lim_{x\rightarrow 0}\dfrac{(1-\cos 2x)\sin 5x}{x^2\sin 3x}=?x→0limx2sin3x(1−cos2x)sin5x=?
limx→π/2sinx−(sinx)sinx1−sinx+Insinx\displaystyle\lim_{x\to \pi/2} \dfrac{sinx-(sinx)^{sin x}}{1-sin x + In sin x}x→π/2lim1−sinx+Insinxsinx−(sinx)sinx is equal to-
এর সঠিক মান কোনটি?