对于某些简单的函数，可以直接将x=0代入公式中求得极限值。例如，limx→0 x^2 = 0^2 = 0。但如果函数在x=0处有不可定义的情况，则不能直接代入。3. 利用基本性质 对于复杂的函数，可以尝试利用基本的极限性质进行转换求解。例如，利用乘除加减的分配律，将复杂的函数转化为几个简单函数求...
lim(x rarr 0)(e^(sinx)-1)/x =lim(x rarr 0)(e^(sinx) cosx)/1 =(e^(sin0) xx cos0) =e^0 =1
Ifl=Limx→0x(1+acosx)−bsinxx3=Limx→01+acosxx2−limx→0bsinxx3, wherel∈R, then View Solution Forx>0,Limx→0[(sinx)1/x+(1x)sinx]is View Solution Evaluatelimx→0tan−1xx View Solution Evaluatelimx→0x3logx View Solution ...
Find \frac{dy}{dx}:\ 17x^{-\frac{1}{2+5\sqrt x Find csc(23). Find y' if sin(xy) = 3xy^{2} + y Find lim_{h→0}\frac{\sqrt{3(a+h)- \sqrt{3a}{h} Let z= \frac{-xy}{5x^2+3y^2} . Find \frac{\partial z}{\partial x} \enspace and \enspace \frac{\...
9.利用等价无穷小的性质求下列极限arctan3.r lim_(x→1)(arctan3x)/(5x) tanr-sin.r(1)lim r)(2) lim_(x→0)(tanx-sinx)/(sin^3x)r0In(1+2.rarcsinr)(3)lim(4)lim rarcsinr tan2r lim_(x→1)(e^(x+1)-1^2-1)/((x^2-1)^2) (6)lim1+x2)(√1+sinr-1) ...
小x-sinx小「ev-e'x(3)lim---•---;(4)lim---*,---r・XT°°x+sinxI”e+e2.1.1Ixsin—20xsin——cos-..解:⑴Vlim---=lim---工不存在,(因sin—,cos一为有界函数)sosinxI。cosxxx2.1xsin-]又lim---=limxsin—=0,2°sinx2°...
Lim(x rarr 0)(tanx sqrt (tanx)-sin x sqrt(sinx))/(x^(3).sqrtx) equals
EvaluateLimx→03sinx−sin3xx−sinx View Solution f(x) is the function such thatLimx→0f(x)x=1. IfLimx→0x(1+acosx)−bsinx(f(x))3=1, then find the value of a and b. View Solution EvaluateLimx→0ex−e−x−2xx−sinx ...
Evaluate the following limit if they exist : limx→24. View Solution Doubtnut is No.1 Study App and Learning App with Instant Video Solutions for NCERT Class 6, Class 7, Class 8, Class 9, Class 10, Class 11 and Class 12, IIT JEE prep, NEET preparation and CBSE, UP Board, Bihar Bo...
Ifl=Limx→0x(1+acosx)−bsinxx3=Limx→01+acosxx2−limx→0bsinxx3, wherel∈R, then View Solution Evaluatelimx→0sinmxsinnx View Solution Evaluatelimx→0tan−1xx View Solution Evaluatelimx→0x3logx Evaluate:limx→0xsinx View Solution ...