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)

Expert Solution

milcah answered 2 years ago

2. Evaluate the following limits. (a) lim x→1+ ln(x) /ln(x − 1) (b) limx→2π x sin(x)...

2. Evaluate the following limits. (a) lim x→1+ ln(x) /ln(x − 1) (b) limx→2π x sin(x) + x ^2 − 4π^2/x − 2π (c) limx→0 sin^2 (3x)/x^2

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

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+

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

Evaluate lim x approaches 0+ x^x^x

USING MATLAB.... a.) Create anonymous functions: fa(x)=sin(x^2) fb(x)=sin^2(x) b.) Evaluate them both at x=1/2 pi c.)Evaluate...

USING MATLAB.... a.) Create anonymous functions: fa(x)=sin(x^2) fb(x)=sin^2(x) b.) Evaluate them both at x=1/2 pi c.)Evaluate them both at x=(0,1,2,...,10)^T d.) Calculate fa(fb(2)) and fb(fa(2))

Each of the following limits represents a derivative f '(a). Find f(x) and a. lim h→0...

Each of the following limits represents a derivative f '(a). Find f(x) and a. lim h→0 (5 + h)3 − 125 h f(x) = a = 5 lim x→2 x3 − 8 x − 2 f(x) = a = 2 lim h→0 52 + h − 25 h f(x) = a = 2

(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)

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!

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