Use LHopital rule to solve. lim (x-1)^(lnx) x goes to 1+

Use LHopital rule to solve.

lim (x-1)^(lnx)
x goes to 1+

Expert Solution

milcah answered 1 year ago

L'Hospitals rule find the limits a) lim (tanx−secx) x→π/2- (b) lim (lnx-1) / (x-e) x→e...

L'Hospitals rule find the limits a) lim (tanx−secx) x→π/2- (b) lim (lnx-1) / (x-e) x→e (c) lim x^(1/lnx) x→0+

Use l'Hopital's rule to find lim x^2/e^x x-> infinity

Use l'Hopital's rule to findlim x^2/e^xx-> infinityUse the right sum with 4 rectangles to approximateIntegral of 2 top x^3dx0 bottom

(a) Consider the function f(x)=(ex −1)/x. Use l’Hˆopital’s rule to show that lim f(x) = 1...

(a) Consider the function f(x)=(ex −1)/x. Use l’Hˆopital’s rule to show that lim f(x) = 1 when x approaches 0 (b) Check this result empirically by writing a program to compute f(x) for x = 10−k, k = 1,...,15. Do your results agree with theoretical expectations? Explain why. (c) Perform the experiment in part b again, this time using the mathematically equivalent formulation, f(x)=(ex −1)/log(ex), evaluated as indicated, with no simplification. If this works any better, can you explain why?...

Evaluate the following limits using l'Hopital's rule. (a) lim x→0 (sin(x)−x)/(x^2) (b) lim x→0 (1/x) −...

Evaluate the following limits using l'Hopital's rule. (a) lim x→0 (sin(x)−x)/(x^2) (b) lim x→0 (1/x) − (1/e^x−1) (c) lim x→0+ (x^√ x)

Evaluate the limit using L'Hôpital's rule lim x → 0 (e^x − x − 1)/2x^2

Determine if exact equation, then solve: x(y+2)y' = lnx+1 , y(1) = -1

lim[(tanx-1)/x] as x->0. lim[ (1+sin(4x))^cot(x)] as x -> 0 from the positive side. lim[ [(a^(1/x) +...

lim[(tanx-1)/x] as x->0. lim[ (1+sin(4x))^cot(x)] as x -> 0 from the positive side. lim[ [(a^(1/x) + b^(1/x))/2]^x] as x -> infinity

Use MuPAD to compute the following limits. a. lim x* x0+ b. lim (cos x)/tan

(a) Find the limit of the following functions: -lim as x approaches 0 (1-cos3(x)/x) -lim as...

(a) Find the limit of the following functions: -lim as x approaches 0 (1-cos3(x)/x) -lim as x approaches 0 (sin(x)/2x) -lim as theta approaches 0 (tan (5theta)/theta) (b) Find the derivative of the following functions: -f(x) = cos (3x2-2x) -f(x) = cos3 (x2/1-x) (c) Determine the period of the following functions: -f(x) = 3 cos(x/2) -f(x)= 21+ 7 sin(2x+3)

1. solve the IVP: xy''-y/x=lnx, on (0, inifnity), y(1)=-1, y'(1)=-2 2.solve the IVP: y''-y=(e^x)/sqrtx, y(1)=e, y'(1)=0...

1. solve the IVP: xy''-y/x=lnx, on (0, inifnity), y(1)=-1, y'(1)=-2 2.solve the IVP: y''-y=(e^x)/sqrtx, y(1)=e, y'(1)=0 3. Given that y1(x)=x is a solution of xy''-xy'+y=0 on (0, inifinity, solve the IVP: xy''-xy'+y=2 on(0,infinity), y(3)=2, y'(3)=1 14. solve the IVP: X'=( 1 2 3) X, X(0)=(0 ##################0 1 4####### -3/8 ##################0 0 1 ########1/4

Question