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

Expert Solution

Note: for any query or explanation in any step kindly mention it in the comment section. I will assist you as soon as possible ?

milcah answered 2 years ago

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)

1) lim (e^x + e^(-x) - 2) / (1 - cos 2x) as x approaches...

1) lim (e^x + e^(-x) - 2) / (1 - cos 2x) as x approaches 0 2) lim sin 5x / 16x as x approaches 0 can someone evaluate the limit

a) Evaluate the limit lim x→0 tan(2x) / x b) Differentiate y = x^tan(x) c) Find...

a) Evaluate the limit lim x→0 tan(2x) / x b) Differentiate y = x^tan(x) c) Find the equation of the tangent line to 4x^2 + 2xy−y^2 = 4 at the point (1, 2). d) Differentiate f(x) = arctan(x^2 + 1) e) Differentiate f(x) = ln(cosh x) Thank you!

A graphing calculator is recommended. For the limit lim x → 2 (x3 − 2x +...

A graphing calculator is recommended. For the limit lim x → 2 (x3 − 2x + 4) = 8 illustrate the definition by finding the largest possible values of δ that correspond to ε = 0.2 and ε = 0.1. (Round your answers to four decimal places.) ε = 0.2 δ = ε = 0.1 δ =

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+

(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) Evaluate the integral from 0 to 1 (e^(2x) (x^2 + 4) dx) (a) What is...

1) Evaluate the integral from 0 to 1 (e^(2x) (x^2 + 4) dx) (a) What is the first step of your ‘new’ integral? (b) What is the final antiderivative step before evaluating? (c) What is the answer in simplified exact form? 2) indefinite integral (cos^2 2theta) / (cos^2 theta) dtheta (a) What is the first step of your ‘new’ integral? (b) What is the simplified integral before taking the antiderivative? (c) What is the answer in simplified form?

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

lim x approaches to 0 ( - cos (x^2) - 1) / e^x^4 - 1 Answer...

lim x approaches to 0 ( - cos (x^2) - 1) / e^x^4 - 1 Answer using l'hopital Please dont skip steps and be detailed with explanation

FInd the limit. 2a) lim (x,y)-->(0,0) (-5x^2)/(2x^2+3y^2) 2b) lim (x,y)-->(0,0) tan(x^2+y^2)arctan(1/(x^2+y^2)) 2c) lim (x,y)-->(2,4) (y^2-2xy)/(y-2x)

Question