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(n/2)(a + l) = n^2 a + l = 2n l = 2n – a l = a + (n-1)d = 2n – a d = 2(n – a)/(n-1) where a would be the first term always.
Diifferentiating y w.r.t. x we get, 2x + 2(y+ xdy/dx) + 4ydy/dx = 0 dy/dx = -(x+y)/(x+2y) = -2 on solving, x + 3y = 0 or x = -3y put in the curve and solve we get y = + 3 and – 3 and x = -9 and +9...
Let y= √(x-1) + √(5-x).Now we will square both sides.y²= x-1 + 5-x + 2√(x-1)√(5-x)Y²= 4 + 2 √-(x²-6x+5)Here,z= x²-5x+6 is a quadratic expression whose range can be calculated by the formula {-D/4a} ....
You can do it by using lim x----> 0 sinx/x=1.Just solve as per this guideline.After putting limit you will get 2x.2x²- 2x-1= 4x³-2x-1. We can`t do it by differentiation as for L Hospital We should...
what if it is not in the form of 0/0? like cosx- log(1+x)/x 2 ? if there is an other way too, please let me know
The expression can be written as:(x + y) / 1 = (dx + dy) / (dx - dy)Using componendo and dividendo:(x + y + 1) / (x + y - 1) = dx/dydy/dx = (x + y - 1) / (x + y + 1)Let x + y = t1 + dy/dx = dt/dx(t -...
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Another has been posted since this image is not clear!! See above this question! Kindly tell answer for that sir!
Its a variable seperable differential equation....divide both sides by y^2... Then integrate both sides then you will get the general solution..just plug in the given conditions and you will get the...
Substitute x= tan(z) in the question then after using identity of cos(2z) u will get the given function as 2∆ I.e. 2*arctan(x) and its differentiation is 2/(1+ x^2)...hope it helps
In this question.. It must be given that the function is a polynomial(which is indirectly given to be proved).. So take a general polynomial of degree n and then subsitute that in the given equation.....
Try desmos (Google it ) ... It is used to graph the function.. Then you can set y as a parameter and then you will see that the function as x-> 0 the graph tends to infinity (for some values of k) and...
there are two ways..... 1> the given function is ln(1+x)=y (by taylor series) … 2> differentiate on both sides then use.... 1 – x + x^2 …..=1/(1+x) by infinte gp formula...hope it helps
I`m probably just being a jerk but you didn`t specify what you are differentiating with respect to.If you differentiate acceleration as a function of distance from (say) the moon, you`ll get a lot...
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