Solution : We have, y = x log x By using product rule in differentiation, \(dy\over dx\) = log x \(dy\over dx\)(x) + x \(dy\over dx\) (log x) \(dy\over dx\) = log x + x/x \(\implies\) \(dy\over dx\) = log x + 1 Hence, the differentiation of x log x with respect to x is …
Solution : We have, y = log ( log x ) By using chain rule in differentiation, \(dy\over dx\) = \(1\over log x\).\(1\over x\) \(\implies\) \(dy\over dx\) = \(1\over x log x\) Hence, the differentiation of log log x with respect to x is \(1\over x log x\). Similar Questions What is the differentiation of …
Solution : On solving the equations 4x + y – 1 = 0 and 7x – 3y – 35 = 0 by using point of intersection formula, we get x = 2 and y = -7 So, given lines intersect at (2, -7) Now, the equation of line joining the point (3, 5) and (2, …
Solution : Solving simultaneously the equations 2x – y + 3 = 0 and x + y – 5 = 0, we obtain \(x\over {5 – 3}\) = \(y\over {3 + 10}\) = \(1\over {2 + 1}\) \(\implies\) \(x\over 2\) = \(y\over 13\) = \(1\over 3\) \(\implies\) x = \(2\over 3\) , y = \(13\over …
Solution : On solving the equations x – 7y + 5 = 0 and 3x + y = 0 by using point of intersection formula, we get x = \(-5\over 22\) and y = \(15\over 22\) So, given lines intersect at \(({-5\over 22}., {15\over 22})\) Let the equation of the required line be x = …
Solution : Inner Radius (r) = \(24\over 2\) = 12 cm Outer Radius (R) = \(28\over 2\) = 14 cm Height of Pipe = 35 cm Volume = \(\pi (R^2 – r^2) h\) = \(\pi \times 52 \times 35\) = 5720 \(cm^3\) Mass of 1 \(cm^3\) wood = 0.6 kg Mass of 5720 \(cm^3\) wood …
Solution : Lateral or Curved Surface Area of Cylinder = \(2 \pi rh\) \(\implies\) \(2 \pi rh\) = 94.2 \(\implies\) \(2 \pi r \times 5\) = 94.2 \(\implies\) r = 3 cm Given, height = 5 cm Volume of Cylinder = \(\pi r^2 h\) = \(\pi \times 9 \times 5\) = \(3.14 \times 9 \times …
Solution : Circumference of the base cylindrical vessel = \(2\pi r\) \(\implies\) \(2\pi r\) = 132 \(\implies\) r = 21 cm Given, height = 25 cm Volume of cylinder = \(\pi r^2 h\) = \(\pi \times {21}^2 \times 25\) = 34650 \(cm^3\) Since 1litre = 1000 \(cm^3\) Therefore, It can hold 34.65 litres of …
Here you will learn what is the formula for volume of cylinder with examples. Let’s begin – What is Cylinder ? Cylinder is a solid which has both of its ends in the form of circle. Its dimensions or sides are defined in the form of the radius of the base (r) and the height …
Formula for Volume of Cylinder – Definition and Examples Read More »
Solution : We have, I = \(sec^{-1}\sqrt{x}\) dx Let x = \(sec^2t\) dx = \(2sec^2 t tan t\) dt I = t.\(2sec^2 t tan t\) dt u = t and v = \(tan^2 t\) I = \(\int\) u.dv = u.v – \(\int\) v.du = \(t.tan^2 t\) – \(\int\) \(tan^2 t\) dt I = \(t.tan^2 t\) …
