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Derivatives of Trigonometric Functions- HW Problems
Evaluate the following limits.
sin(3𝑥)
1. lim
𝑥→0 2𝑥
sin(6𝑥)
2. lim
𝑥→0 sin(2𝑥)
tan(4𝑥)
3. lim
𝑥→0 sin(6𝑥)
sin(2𝑥)
4. lim
𝑥→0 2𝑥2 −4𝑥
(cos2 𝑥)(tan2 𝑥)
5. lim
𝑥→0 6𝑥2
Find the derivatives of the following functions.
6. 𝑓(𝑥 ) = 𝑠𝑖𝑛𝑥 − 4𝑐𝑜𝑠𝑥 + 3𝑡𝑎𝑛𝑥
𝑠𝑖𝑛𝑥
7. 𝑓(𝑥 ) = 𝑥𝑐𝑜𝑠𝑥 −
𝑥2
8. 𝑔(𝑥 ) = cos2 𝑥 = (cos(𝑥 ))(cos(𝑥 ))
tan (𝑡)
9. 𝑓(𝑡) = 𝑡𝑐𝑠𝑐 (𝑡) −
𝑡2
10. 𝑔(𝑡) = (sec(𝑡))(cot(𝑡))
sin(𝜃)
11. 𝑓 (𝜃 ) =
1+cos(𝜃)
𝑥𝑐𝑜𝑠(𝑥)
12. 𝑔(𝑥 ) =
1+𝑥
13. 𝑓 (𝑥 ) = 2𝑠𝑒𝑐 (𝑥 ) − 𝑥 2 cot(𝑥 )
Derivatives of Trigonometric Functions- HW Problems
Evaluate the following limits.
sin(3𝑥)
1. lim
𝑥→0 2𝑥
sin(6𝑥)
2. lim
𝑥→0 sin(2𝑥)
tan(4𝑥)
3. lim
𝑥→0 sin(6𝑥)
sin(2𝑥)
4. lim
𝑥→0 2𝑥2 −4𝑥
(cos2 𝑥)(tan2 𝑥)
5. lim
𝑥→0 6𝑥2
Find the derivatives of the following functions.
6. 𝑓(𝑥 ) = 𝑠𝑖𝑛𝑥 − 4𝑐𝑜𝑠𝑥 + 3𝑡𝑎𝑛𝑥
𝑠𝑖𝑛𝑥
7. 𝑓(𝑥 ) = 𝑥𝑐𝑜𝑠𝑥 −
𝑥2
8. 𝑔(𝑥 ) = cos2 𝑥 = (cos(𝑥 ))(cos(𝑥 ))
tan (𝑡)
9. 𝑓(𝑡) = 𝑡𝑐𝑠𝑐 (𝑡) −
𝑡2
10. 𝑔(𝑡) = (sec(𝑡))(cot(𝑡))
sin(𝜃)
11. 𝑓 (𝜃 ) =
1+cos(𝜃)
𝑥𝑐𝑜𝑠(𝑥)
12. 𝑔(𝑥 ) =
1+𝑥
13. 𝑓 (𝑥 ) = 2𝑠𝑒𝑐 (𝑥 ) − 𝑥 2 cot(𝑥 )
