Skip to main content

Hitungan: Untuk f (t) = (t / e ^ (1-3t), 2t ^ 2-t) berapa jarak antara f (2) dan f (5)? - 2020

Anonim

Menjawab:

#sqrt (25 e ^ (28) - 20 e ^ (19) + 4 e ^ (10) + 1521) #

Penjelasan:

Kita punya: #f (t) = ((t) / (e ^ (1 - 3 t)), 2 t ^ (2) - t) #

Pertama, mari kita evaluasi #f (2) # dan #f (5) #:

# => f (2) = ((2) / (e ^ (1 - 3 cdot 2)), 2 cdot 2 ^ (2) - 2) #

# => f (2) = ((2) / (e ^ (1 - 6)), 2 cdot 4 - 2) #

# => f (2) = ((2) / (e ^ (- 5)), 8 - 2) #

#therefore f (2) = (2 e ^ (5), 6) #

dan

# => f (5) = ((5) / (e ^ (1 - 3 cdot 5)), 2 cdot 5 ^ (2) - 5) #

# => f (5) = ((5) / (e ^ (1 - 15)), 2 cdot 25 - 5) #

# => f (5) = ((5) / (e ^ (- 14)), 50 - 5) #

#therefore f (5) = (5 e ^ (14), 45) #

Lalu, mari kita evaluasi jarak antara dua titik ini:

# => d = sqrt ((5 e ^ (14) - 2 e ^ (5)) ^ (2) + (45 - 6) ^ (2)) #

# => d = sqrt ((25 e ^ (28) - 20 e ^ (19) + 4 e ^ (10)) + 39 ^ (2)) #

#therefore d = sqrt (25 e ^ (28) - 20 e ^ (19) + 4 e ^ (10) + 1521) #