Maths-
General
Easy
Question
If ![f left parenthesis x right parenthesis equals negative square root of 25 minus x squared end root comma text then end text L t subscript x not stretchy rightwards arrow 1 end subscript fraction numerator f left parenthesis x right parenthesis minus f left parenthesis 1 right parenthesis over denominator x minus 1 end fraction equals](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAUgAAAAlCAYAAAAgCXADAAAACXBIWXMAAA7EAAAOxAGVKw4bAAAABGJhU0UAAAAZpE86XgAABk9JREFUeNrtnV9oHUUUxocQQpAiiJVaiqSEEIpIKZQQqxYRSymhiAh9KL40REopRYovfbFY6INFIS3FtyhBRAJFgmiRgoiGEIpUStGqReiTlOpLhFhqaCvtOdxzyebu7O7M7s7OzL3fDw692dndnszMfjt/zrlRCgDQbRwlO2N5zRm5LhafffsLAAicPrJNHce2k10ueb8luT4Wn5vwFwAQIfvIlsWuk/UnRGNHyXvuJFsMyOdRspNk1zz5CwCIEBaWWwlReVb+3SFiU4VFEZ4QfP6M7DDZQw/+AgAi5Q2yOc3xD8iOVbz328p+/dK1zw89+AssGJRG6jUDYfIe2QnN8UtkuzXHpzJE5LSUJdlF9l0APpsKpCt/geXayRVUAwiA+Y6X2MFE2QrZQMZ1V9X6zZFJso805w3IfULw2UQgXfgLLDlL9j6qAQTCDbJnNMcfFLzkp+XznoJR171AfDYRSFf+Agt+J3se1QACgMNk7maUFYnNt2Qvq9au8JMlBKfsskwVnyGQgbOV7B+1FpLQLbQ7NHcu3kUcQVNHwTjZ9xllRdPV49Le2xueslbxGVPswOEdtrkuH5FwRsJVNHUU8PrdbM4I8cWMMj7+hUyzD+bc38WmR1mfTQQyqE2aGFOYqvI12aEeePBWoT1RcF61YgN1ZIXMDJN9RfYY2Qayn3Km2MfkPr59NhVIF/4ajSpiS2FyAU+r/yV7ussfOl6XWoD2RAHvCE9klOmCrp8i+6ZDEPerVhC2DheB17Y+2whk44HiMaYwuayLKwVTFl7/4HUdXvh+M6NxQ44z3CxtO+zg3qHFUt6Vl3/M8HM5mFN+OTEYGRBx2qI5b076dxPPqY3PRc+OV12JMYXJJR+qVjCtjgVZW9mQqKsllV7fCTngmnNdL4pIVn0AQhdI3oT6uaB8KfD+yKPB2wXnhDbTc+lz4zPTGFOYXMLhPS9ZnD+keQhDFcjNMvV63OFIMaTf/XWVv9nGff/zgPviOdWKJTR5ho6UeNb4GT8ckc8u/C0kxhQmV2xV5cJ7Vj2LhGmbsDhuq0kcs6ZA7Z8nZISwKiNvXcAwj7z/lHNmNVOy9r0OkN0suJdN326XJX+HEwH2x50i4jERo8+Z+Exh8p0XvDHjjWYb3rNLM03zMYoyaZM66zhvBDnVIcaTKr0hNK7WMi36ZGQwrbnXARk5DOXcK4sLMoosWw7ip7LOxJjCVIURGa1wxYx1lNmG9/CI50eVjulqB2OviFC8o9bWLV1h0yZ1dbys453T1j5NP5hX6bXb25p7vWJwryz+UPrNimTfH4KGgCx8pjD5eju8KwL5lywjJMWOp9em4T1PkH1JtjfnnH6ZcpyUh3GbyzedRZu4FshBg/PvqHRY2YrF/2HSt++U7PuxjHxgjmebPlOYfE+x2f//Eg8zj7p+Mbx2WMTRJlVvr3Ifd2jSJk0IpMlxkzavIpB5fbtdjjhQTLFz+1KMKUx1cp/sLfnM4T2nDK7hUeCMamUo2OIyc8W0TUIRyGWDOqwikHl9u13+qce+V/SnBUAAxJjCVCc/kP0qn02+vYenhBdUuS+xeE61dmJdYNMmdXFP6QOwTUWNxWvKoUBy357MKT+nqoexVcHkTwsAz8SYwlQnr5L9T/aCam0QFAnfRWUWJjMvo+c+sX0iji7CH2zbxIQ5eXDzdnivZYxUTUVtROqkvYY7pBnRVRHIeZXOGknCO/yf5JQvJpYquA0vKfMNnVllvikHgQyYGFOY6oY3Zm4os/Ae03UMDk3hHdQHUsc86hxz4Lttm9QpkLy7/Leqtm44Ji9hridOcX2tRoFczmkrrjfOgrqV+LmT/Yk+MW35cpuR9h+HQMZLjClMLvhYOukhdImUSE70eB3wKPm4CJ6OowUvTRb+0R4XyCjXWmNMYXLFJumkG6GJ65ZXrqvu+8JgW87LczJged2MLB+YzBq6XSCjXGvtqnSgGjiCKljHFpWOUew19sgo+jeZbdmANUgsJXQV/agCkIAzyxZE5HgafbpLhMPmexQgkACAFDyd5s3F0cTPN1X9qaK+vivU9HsUIJAAgJ6j6Zx9CCQAICpscvbrSgmGQAIAoqDJnH0IJAAgGprO2YdAAgCiwEfOPgQSABA8LnL2IZAAgOhxlbNvKowh/unjTB4B3lzSoR+c/vIAAAIUdEVYdE1hdGhNTAA8bWF0aCB4bWxucz0iaHR0cDovL3d3dy53My5vcmcvMTk5OC9NYXRoL01hdGhNTCI+PG1pPmY8L21pPjxtbz4oPC9tbz48bWk+eDwvbWk+PG1vPik8L21vPjxtbz49PC9tbz48bW8+JiN4MjIxMjs8L21vPjxtc3FydD48bW4+MjU8L21uPjxtbz4mI3gyMjEyOzwvbW8+PG1zdXA+PG1pPng8L21pPjxtbj4yPC9tbj48L21zdXA+PC9tc3FydD48bW8+LDwvbW8+PG10ZXh0PiYjeEEwO3RoZW4mI3hBMDs8L210ZXh0PjxtaT5MPC9taT48bXN1Yj48bWk+dDwvbWk+PG1yb3c+PG1pPng8L21pPjxtbyBzdHJldGNoeT0iZmFsc2UiPiYjeDIxOTI7PC9tbz48bW4+MTwvbW4+PC9tcm93PjwvbXN1Yj48bWZyYWM+PG1yb3c+PG1pPmY8L21pPjxtbz4oPC9tbz48bWk+eDwvbWk+PG1vPik8L21vPjxtbz4mI3gyMjEyOzwvbW8+PG1pPmY8L21pPjxtbz4oPC9tbz48bW4+MTwvbW4+PG1vPik8L21vPjwvbXJvdz48bXJvdz48bWk+eDwvbWk+PG1vPiYjeDIyMTI7PC9tbz48bW4+MTwvbW4+PC9tcm93PjwvbWZyYWM+PG1vPj08L21vPjwvbWF0aD60XK/IAAAAAElFTkSuQmCC)
Hint:
In the question first we will use the L hospital theorem, then after putting the value of f(x) we will get the answer.
The correct answer is: ![fraction numerator 1 over denominator square root of 24 end fraction](data:image/png;base64,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)
Given, ![f left parenthesis x right parenthesis equals negative square root of 25 minus x squared end root](data:image/png;base64,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)
![L t subscript x not stretchy rightwards arrow 1 end subscript fraction numerator f left parenthesis x right parenthesis minus f left parenthesis 1 right parenthesis over denominator x minus 1 end fraction
u sin g space L space h o s p i t a l space t h e o r e m comma
equals L t subscript x not stretchy rightwards arrow 1 end subscript fraction numerator begin display style fraction numerator d blank over denominator d x end fraction end style f left parenthesis x right parenthesis minus f left parenthesis 1 right parenthesis over denominator begin display style fraction numerator d blank over denominator d x end fraction end style x minus 1 end fraction
equals L t subscript x not stretchy rightwards arrow 1 end subscript fraction numerator f apostrophe left parenthesis x right parenthesis over denominator 1 end fraction
equals L t subscript x not stretchy rightwards arrow 1 space end subscript f apostrophe left parenthesis x right parenthesis
equals L t subscript x not stretchy rightwards arrow 1 space end subscript fraction numerator d left parenthesis negative square root of 25 minus x squared end root right parenthesis over denominator d x end fraction
equals L t subscript x not stretchy rightwards arrow 1 space end subscript fraction numerator negative 1 cross times negative 2 over denominator 2 square root of 25 minus x squared end root end fraction
equals L t subscript x not stretchy rightwards arrow 1 space end subscript fraction numerator 1 over denominator square root of 25 minus x squared end root end fraction
equals fraction numerator 1 over denominator square root of 25 minus 1 end root end fraction
equals fraction numerator 1 over denominator square root of 24 end fraction](data:image/png;base64,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Related Questions to study
maths-
maths-General
Maths-
If
then the values of a and b are
If
then the values of a and b are
Maths-General
Maths-
Maths-General
Maths-
If
then k=
If
then k=
Maths-General
maths-
Let
and
be the distinct roots of
then ![fraction numerator L t over denominator x plus a end fraction fraction numerator 1 minus cos space open parentheses a x squared plus b x plus c close parentheses over denominator left parenthesis x minus alpha right parenthesis squared end fraction](data:image/png;base64,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)
Let
and
be the distinct roots of
then ![fraction numerator L t over denominator x plus a end fraction fraction numerator 1 minus cos space open parentheses a x squared plus b x plus c close parentheses over denominator left parenthesis x minus alpha right parenthesis squared end fraction](data:image/png;base64,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)
maths-General
Maths-
In ![straight capital delta A B C comma sum a cubed sin invisible function application left parenthesis B minus C right parenthesis equals](data:image/png;base64,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)
In ![straight capital delta A B C comma sum a cubed sin invisible function application left parenthesis B minus C right parenthesis equals](data:image/png;base64,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)
Maths-General
maths-
maths-General
Maths-
In ![straight capital delta A B C comma a squared cot invisible function application A plus b squared cot invisible function application B plus C squared cot invisible function application C equals](data:image/png;base64,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)
In ![straight capital delta A B C comma a squared cot invisible function application A plus b squared cot invisible function application B plus C squared cot invisible function application C equals](data:image/png;base64,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)
Maths-General
Maths-
Maths-General
Maths-
Maths-General
Maths-
In ![straight triangle A B C comma cot invisible function application A over 2 plus cot invisible function application B over 2 plus cot invisible function application C over 2 equals](data:image/png;base64,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)
In ![straight triangle A B C comma cot invisible function application A over 2 plus cot invisible function application B over 2 plus cot invisible function application C over 2 equals](data:image/png;base64,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)
Maths-General
Maths-
Maths-General
Maths-
Maths-General
Maths-
In
, cot ![A plus cot invisible function application B plus cot invisible function application C equals](data:image/png;base64,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)
In
, cot ![A plus cot invisible function application B plus cot invisible function application C equals](data:image/png;base64,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)
Maths-General
Maths-
Maths-General