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lim(yto0) ((x+y)sec(x+y)-xsecx)/(y) is e...

`lim_(yto0) ((x+y)sec(x+y)-xsecx)/(y)` is equal to

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The correct Answer is:
A
`underset(yto0)lim{(x{sec(x+y)-secx})/(y)+sec(x+y)}`
`=underset(yto0)lim[(x)/(y){(cosx-cos(x+y))/(cos(x+y)cosx)}]+underset(yto0)limsec(x+y)`
`=underset(yto0)lim[(x2sin(x+(y)/(2))sin((y)/(2)))/(ycos(x+y)cosx)]+secx`
`=underset(yto0)lim[(xsin(x+(y)/(2)))/(cos(x+y)cosx)xx(sin((y)/(2)))/((y)/(2))]+secx`
`=xtanxsecx+secx`
`=secx(xtanx+1)`
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CENGAGE-LIMITS-Exercise (Single)
  1. lim(xto1) (1-x^(2))/(sin2pix) is equal to

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  2. lim(xto0) (1)/(x)cos^(1)((1-x^(2))/(1+x^2)) is equal to

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  3. lim(yto0) ((x+y)sec(x+y)-xsecx)/(y) is equal to

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  4. lim(xto1) (1+sinpi((3x)/(1+x^(2))))/(1+cospix) is equal to

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  5. lim(ntooo) sum(x=1)^(20)cos^(2n)(x-10) is equal to

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  6. lim(xto-1) ((x^(4)+x^(2)+x+1)/(x^(2)-x+1))^((1-cos(x+1))/(x+1)^(2)) is...

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  7. lim(xtooo) {(x+5)tan^(-1)(x+5)-(x+1)tan^(-1)(x+1)} is equal to

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  8. The value of lim(xto0) ([(100x)/(sinx)]+[(99sinx)/(x)]) (where [.] rep...

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  9. The value of lim(xtoa) sqrt(a^(2)-x^(2))"cot"(pi)/(2)sqrt((a-x)/(a+x))...

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  10. lim(xto0) [min(y^(2)-4y+11)(sinx)/(x)] (where [.] denotes the greatest...

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  11. The value of lim(xto0) (1-(cosx)sqrt(cos2x))/(x^(2)) is

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  12. lim(xtooo) (1)/(x+1)tan((pix+1)/(2x+2)) is equal to

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  13. The value of lim(xto1^(-)) (1-sqrt(x))/((cos^(-1)x)^(2)) is

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  14. lim(xto pi//2) (sin(xcosx))/(cos(xsinx)) is equal to

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  15. lim(xto0) [(1-e^(x))(sinx)/(|x|)] is (where [.] represents the greates...

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  16. Evaluate lim(xto0) (x(e^(x)-1))/(1-cosx) is equal to

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  17. If f(x)=lim(ntooo) n(x^(1//n)-1)," then for "xgt0, ygt0,f(xy) is equal...

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  18. lim(x to 0) {(1+x)^((2)/(x))} (where {.} denotes the fractional part o...

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  19. The value of lim(xtooo) ((2^(x^(n)))e^((1)/(x))-(3^(x^(n)))e^((1)/(x))...

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  20. lim(x to 0) (sin(x^(2)))/("ln"(cos(2x^(2)-x))) is equal to

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