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3 years ago

Does anyone know how to do this? I’m confused

Mathematics

2 answers:

nikklg [1K]3 years ago

5 0

Answer:

cos(θ)

Step-by-step explanation:

Para una función f(x), la derivada es el límite de

f(x+h)−f(x)

, ya que h va a 0, si ese límite existe.

dθ

(sin(θ))=(

h→0

lim

sin(θ+h)−sin(θ)

)

Usa la fórmula de suma para el seno.

h→0

lim

sin(h+θ)−sin(θ)

Simplifica sin(θ).

h→0

lim

sin(θ)(cos(h)−1)+cos(θ)sin(h)

Reescribe el límite.

(

h→0

lim

sin(θ))(

h→0

lim

cos(h)−1

)+(

h→0

lim

cos(θ))(

h→0

lim

sin(h)

)

Usa el hecho de que θ es una constante al calcular límites, ya que h va a 0.

sin(θ)(

h→0

lim

cos(h)−1

)+cos(θ)(

h→0

lim

sin(h)

)

El límite lim

θ→0

sin(θ)

es 1.

sin(θ)(

h→0

lim

cos(h)−1

)+cos(θ)

Para calcular el límite lim

h→0

cos(h)−1

, primero multiplique el numerador y denominador por cos(h)+1.

(

h→0

lim

cos(h)−1

)=(

h→0

lim

h(cos(h)+1)

(cos(h)−1)(cos(h)+1)

)

Multiplica cos(h)+1 por cos(h)−1.

h→0

lim

h(cos(h)+1)

(cos(h))

−1

Usa la identidad pitagórica.

h→0

lim

−

h(cos(h)+1)

(sin(h))

Reescribe el límite.

(

h→0

lim

−

sin(h)

)(

h→0

lim

cos(h)+1

sin(h)

)

El límite lim

θ→0

sin(θ)

es 1.

−(

h→0

lim

cos(h)+1

sin(h)

)

Usa el hecho de que

cos(h)+1

sin(h)

es un valor continuo en 0.

(

h→0

lim

cos(h)+1

sin(h)

)=0

Sustituye el valor 0 en la expresión sin(θ)(lim

h→0

cos(h)−1

)+cos(θ).

cos(θ)

bonufazy [111]3 years ago

5 0

Answer:

B. 9/41

Step-by-step explanation:

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