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The value of lim(xrarrpi//4) (tan^(3)x-t...

The value of `lim_(xrarrpi//4) (tan^(3)x-tanx)/(cos(x+(pi)/(4)))` is

A

8

B

4

C

`-8`

D

`-2`

Text Solution

Verified by Experts

The correct Answer is:
C
We have, `underset(xrarrpi//4)(lim)(tan^(3)x-tanx)/(4cos(x+pi//4))`
`=underset(xrarrpi//4)(lim)(tanx(tanx-1)(tanx+1))/(cos(x +pi//4))`
`=underset(xrarrpi//4)(lim)(tanx(sinx-cosx)(tanx+1))/(cosx cos(x+pi//4))`
`=-underset(xrarrpi//4)(lim)(tanx(cosx-sinx)(tanx+1))/(cosx cos(x+pi//4))`
`=-sqrt2underset(xrarrpi//2)(lim)(tanx((1)/(sqrt2)cosx-(1)/(sqrt2)sinx)(tanx+1))/(cosx cos(x+pi//4))`
`=-sqrt2underset(xrarrpi//4)(lim)(tanx(tanx+1))/(cosx)`
`=-sqrt2xx2xxsqrt2=-8`
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CENGAGE-LIMITS-Single Correct Answer Type
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  3. The value of lim(xrarrpi//4) (tan^(3)x-tanx)/(cos(x+(pi)/(4))) is

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  4. lim(xrarr(pi)/(2)) ((1-sinx)(8x^(3)-pi^(3)))/(pi-2x)^(4)

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  5. lim(xrarroo) (sum(r=1)^(10)(x+r)^(2010))/((x^(1006)+1)(2x^(1004)+1))=

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  6. If lim(xrarr0) (f(x))/(x^(2))=a and lim(xrarr0) (f(1-cosx))/(g(x)sin^(...

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  7. If f(x)={{:((x)/(sinx)",",x gt0),(2-x",",xle0):}andg(x)={{:(x+3",",xlt...

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  8. If k in I such that lim(nrarroo) (cos.(kpi)/(4))^(2n)-(cos.(kpi)/(6))^...

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  9. If a(n) and b(n) are positive integers and a(n)+sqrt2b(n)=(2+sqrt2))^(...

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  10. The value of (lim(x rarr 0) (tanx^((1)/(5)))/((tan^(-1)sqrtx)^(2))(log...

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  11. The value of lim(xrarr3) ((x^(3)+27)log(e)(x-2))/(x^(2)-9) is

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  12. The value of lim(xrarr0^(+))((1-cos(sin^(2)x))/(x^(2)))^((log(e)(1-2x^...

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  13. lim(xrarr0) (1)/(x^(2))|(1-cos3x,log(e)(1+4x)),(sin^(-1)(x^(x)-),tan^(...

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  14. If graph of the function y=f(x) is continuous and passes through point...

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  15. Let f(x) be defined for all x in R such that lim(xrarr0) [f(x)+log(1-(...

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  16. lim(xrarroo) x^(2)sin(log(e)sqrt(cos(pi)/(x)))

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  17. If lim(xrarroo) ((x+c)/(x-c))^(x)=4 then the value of e^(c) is

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  18. If lim(xrarr0) [1+x+(f(x))/(x)]^(1//x)=e^(3)", then "lim(xrarr0) [1+(f...

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  19. lim(xrarr(pi^(-))/(2)) [1+(cosx)^(cosx)]^(2)=

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  20. If agt0, b gt0 than lim(nrarroo) ((a-1+b^((1)/(n)))/(a))^(n)=

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