Maths-
General
Easy
Question
The value of ![stretchy integral subscript 0 end subscript superscript 1 end superscript fraction numerator l o g subscript e end subscript invisible function application left parenthesis x plus 1 right parenthesis over denominator 1 plus x to the power of 2 end exponent end fraction d x text is end text](data:image/png;base64,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)
- 0
The correct answer is: ![fraction numerator pi I n invisible function application 2 over denominator 8 end fraction](data:image/png;base64,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)
Related Questions to study
maths-
If function f(x)
is equal to
If function f(x)
is equal to
maths-General
maths-
If
then
If
then
maths-General
maths-
Statement - I :
attain its maximum value ![text at end text x equals fraction numerator pi over denominator 3 end fraction](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAEgAAAAfCAYAAABEZosIAAAACXBIWXMAAA7EAAAOxAGVKw4bAAAABGJhU0UAAAATRJrTQAAAAdxJREFUeNrtmjFIAlEYx4+QiGiJCIdoiaYGaYkIiRAaIiQiiGgKaWtya2oICZqkIYKmiIiWaIiIICIahRCHBhGiMVoaJEIkuP4P/5evS0/Lu/Ly+8EP7l2J9ee9933v1DBahxX4Ck0HV40WZh/2w2M4q91X46ghfHDPoCweYFBiKRHgMtPHLxJLmTF4bRtfSSxlFuGeNl7g3iSQHRjTxgm4LbF83qCHtfEGvISDsNPtN3v2WTiqtKdt90ZgHh548YZmq0/HGZiCRZiDYVs4urVYhpsV7if4M19yCId4rTa2uwZnUNrWkMVqbJBmHTYNbZxJjQQ0BZO8nvyP/Yfpwh6kKsYEzMAej//WRq3JGveetyov+klAcc7EkEv/5J+xC+dhh4szKMyTc5Idra/J17HEityb6mEAnrIZ64K3Hi8xz8lq5beP5fiR1xaZOmdCLzy3BRL1qjn7LUIsy0X2QqNwHT5pvxPh2GmptcMTW7AWR6xsQpMQ4UxWz4MKLEBbfl/qbqKeA81xVluog+uFRPP9giRo1TUrMXwlyLOg2oemJY7q3XlcIqlMt1F6gJbi2VCoQhdDEhwoSATOJ4acxFDihk8oAjxkq85afey8JNGUGIdnXFIFdtY1v7TwDjvSjI1v0SOyAAAAmXRFWHRNYXRoTUwAPG1hdGggeG1sbnM9Imh0dHA6Ly93d3cudzMub3JnLzE5OTgvTWF0aC9NYXRoTUwiPjxtdGV4dD4mI3hBMDthdCYjeEEwOzwvbXRleHQ+PG1pPng8L21pPjxtbz49PC9tbz48bWZyYWM+PG1pPiYjeDNDMDs8L21pPjxtbj4zPC9tbj48L21mcmFjPjwvbWF0aD5DhKfxAAAAAElFTkSuQmCC)
Statement - 2:
increasing function in ![open square brackets fraction numerator pi over denominator 6 end fraction comma fraction numerator pi over denominator 3 end fraction close square brackets text . end text](data:image/png;base64,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)
Statement - I :
attain its maximum value ![text at end text x equals fraction numerator pi over denominator 3 end fraction](data:image/png;base64,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)
Statement - 2:
increasing function in ![open square brackets fraction numerator pi over denominator 6 end fraction comma fraction numerator pi over denominator 3 end fraction close square brackets text . end text](data:image/png;base64,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)
maths-General
maths-
denotes the greatest integer function, is continuous and differentiable in (4, 6) then.
denotes the greatest integer function, is continuous and differentiable in (4, 6) then.
maths-General
maths-
denotes greatest integer function)
denotes greatest integer function)
maths-General
maths-
If graph of the function y= f(x) is continuous and passes through point (3, 1) then ![stack l i m with x rightwards arrow 3 below blank fraction numerator l n left parenthesis 3 f left parenthesis x right parenthesis minus 2 right parenthesis over denominator 2 left parenthesis 1 minus f left parenthesis x right parenthesis right parenthesis end fraction text is equal end text](data:image/png;base64,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)
If graph of the function y= f(x) is continuous and passes through point (3, 1) then ![stack l i m with x rightwards arrow 3 below blank fraction numerator l n left parenthesis 3 f left parenthesis x right parenthesis minus 2 right parenthesis over denominator 2 left parenthesis 1 minus f left parenthesis x right parenthesis right parenthesis end fraction text is equal end text](data:image/png;base64,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)
maths-General
maths-
A function f from integers to integers is defined as
then the sum of digits k is
A function f from integers to integers is defined as
then the sum of digits k is
maths-General
maths-
Let f(x)
a prime number. The number of points at which f(x) is non-differentiable is ( [.] G.I.F )
Let f(x)
a prime number. The number of points at which f(x) is non-differentiable is ( [.] G.I.F )
maths-General
maths-
If graph of the function y= f(x) is continuous and passes through point (3, 1) then
is equal
If graph of the function y= f(x) is continuous and passes through point (3, 1) then
is equal
maths-General
maths-
Let f be twice differentiable real valued function satisfying
where
and
then
Statement -1:![vertical line f left parenthesis x right parenthesis vertical line less or equal than 5 for all x greater than 0](data:image/png;base64,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)
Statement -2:
is decreasing ![for all x greater than 0.](data:image/png;base64,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)
Let f be twice differentiable real valued function satisfying
where
and
then
Statement -1:![vertical line f left parenthesis x right parenthesis vertical line less or equal than 5 for all x greater than 0](data:image/png;base64,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)
Statement -2:
is decreasing ![for all x greater than 0.](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAADgAAAAOCAYAAAB6pd+uAAAACXBIWXMAAA7EAAAOxAGVKw4bAAAABGJhU0UAAAANvpXuIwAAAZlJREFUeNpjYEAFV4BYhQE7AIlfYhjioBmIi3DIFUHlBxLwAfE0ID4JxTOhYkQDUyA+iENuPxCbD7AH9wKxHxLfBypGEngKxIJYQu45FR0KCkRrEvWEAvEkLOITgDiSFIPWAPF/LHgNDvXJQNyBI7kn49BjCQ15UjwKst8Ni7gjHrdhBaBoX4UmtgoqjgucA2JxJH4iEE8hwi5kj1oSUPsOiNmwiIPEXpLiQRYg/gSlYfwvQMyER48HEPdB2S5k5AuYR/fj8egfPPp/kZpHliNlZmwxig3sBmJ7IL4AxMJk5s0iaHYg1YM/SLUoGohnQ9mzoXxCoAAaknpkeMwSGnv4YvAljiTKQWoSRS81sZWq6MAamtH7SCzRYB47TEQeXAPNCujAjdRCBrney8FTL8KAEhBvAmIuIOYB4jNEJFFkj9kS6Z4gpFSFDOaTWk0g54eneFo2ICAKxNvQPATKs4sJmE2Kx9ADvQBa8IGSazWOCPiPJy+jxMx/PG1TkAXrgFgaRyHlQYOWDCirzIUWKt+gTTUecj04LAAA6hNZmwik224AAAB7dEVYdE1hdGhNTAA8bWF0aCB4bWxucz0iaHR0cDovL3d3dy53My5vcmcvMTk5OC9NYXRoL01hdGhNTCI+PG1vPiYjeDIyMDA7PC9tbz48bWk+eDwvbWk+PG1vPiZndDs8L21vPjxtbj4wPC9tbj48bW8+LjwvbW8+PC9tYXRoPvtBiXwAAAAASUVORK5CYII=)
maths-General
maths-
Let
Then which one of the following is true ?
Let
Then which one of the following is true ?
maths-General
maths-
andE..
then-
andE..
then-
maths-General
maths-
If for a non-zero x, af
where
then
f(x)dx=
If for a non-zero x, af
where
then
f(x)dx=
maths-General
chemistry-
Which of the following is correct?
Which of the following is correct?
chemistry-General
chemistry-
In the thermal power stations, electricity is produced by producing heat energy from the burning of coal. This is an example of ..
In the thermal power stations, electricity is produced by producing heat energy from the burning of coal. This is an example of ..
chemistry-General