Skip to document
Welcome to StudocuSign in to access the best study resources
Guest user
0followers
HomeMy LibraryAsk AI
  • You don't have any recent items yet.
My Library
  • You don't have any courses yet.
  • You don't have any books yet.
  • You don't have any Studylists yet.

Math 11-Worksheet 06 - worksheet

worksheet
Course

Calculus I (MATH 011)

81 Documents
Students shared 81 documents in this course
Academic year: 2022/2023
Uploaded by:
Anonymous Student
This document has been uploaded by a student, just like you, who decided to remain anonymous.
University of California, Merced

Comments

Please sign in or register to post comments.

Students also viewed

Related documents

Preview text

Math 11 Worksheet 6 for Sections 3, 3, and 3 Spring 2023

1 Section 3.

  1. For each function, (i) compute the derivative and (ii) evaluate this at the given point. (a) f (x) = (x 2 + 1)(x − 1), x = − 1 (b) g(x) = (x 3 + 2x − 1)(x + 2), x = 0 (c) h(x) = (x 2 − 2 x + 3)(1 − 3 x + 2x 2 ), x = 1
  2. For each function, (i) compute the derivative and (ii) evaluate this at the given point. You may use the work done in previous problems, if applicable. (a) f (x) = x x 2 −+ 1 1 , x = 0 (b) g(x) = x 3 + 2 x + 2x − 1 , x = − 1 (c) h(x) = 1 x − 2 − 3 x 2 x+ 2 + 3x 2 , x = 2
  3. For each function, (i) compute the derivative and (ii) evaluate this at the given point. You may use the work done in previous problems, if applicable. You need not simplify the results. (a) f (x) = (x 2 + 1)(x − 1) 2 , x = − 1 (b) g(x) = x(x 3 + 2x − 1)(x + 2), x = 0 (c) h(x) = (x 1 + 1)(− 3 x x+ 2 2 + 3)x 2 , x = 2 (d) r(x) = (x 2 − x + 1)( x 2 −+3 + 2 x x − x 2 ), x = 1
  4. Compute the derivatives of the following functions. (a) B(x) = −x− 11 (b) C(x) = x 3 / 4 (c) D(t) = 1 t 5 (d) E(x) = √ 3 x

(e) F (x) =

√ 1

x 3 (f) H(x) = 5 √ 5 x 4 + x 12 (g) I(t) = 3t 5 − 5 √t + 7 t (h) J(t) = t 3 / 2 (2 + √t)

(i) K(x) = x 2 x+ 1 (j) L(θ) = θ √−θ 1 (k) M (x) = ax c+ b (where a, b, c are constants)

1

Math 11 Worksheet 6 for Sections 3, 3, and 3 Spring 2023

  1. Find the equation of the tangent line to the given function at the indicated point. (a) f (x) = 1 − 2 x 1 / 3 at x = − 1 (b) g(x) =

√x − x √x at x = 4

(c) h(x) = x 42 − 1 x + 2 at x = 2

2 Section 3.

  1. Find the derivative of each of the following functions. (a) f (x) = 2 sin x − 3 cos x (b) g(θ) = sin θ cos θ (c) h(t) = t 2 cos t − t sin t

(d) p(x) = (1 + cos x) 2 (e) r(θ) = 1 1 + cos − sin θθ 2. Find the derivative of each of the following functions. (a) f (x) = 2 sec x − 3 csc x (b) g(θ) = sec θ csc θ (c) h(t) = t 2 tan t − t cot t

(d) p(x) = (1 + tan x) 2 (e) r(θ) = 1 1 + cot − sec θθ 3. Find the equation of the tangent line to the given function at the indicated point. (a) f (t) = 1 − 2 sin t at t = π (b) g(x) = sin x cos − xcos xat x = π/ 4

(c) h(θ) = tan 2 θ at θ = 3π/ 4 (d) r(x) = (1 − cot x) 2 at x = π/ 2

3 Section 3

  1. Compute the average acceleration, aavg, for the given position, s(t), or velocity, v(t), function over the given interval. (a) v(t) = t 2 over t = 3 to t = 10 (b) s(t) = t 2 over t = 3 to t = 10 (c) v(t) = cos t over t = 0 to t = π/ 2

(d) s(t) = 50 − √t over t = 9 to t = 25 (e) v(t) = ln t over t = 1 to t = e 2 (f) s(t) = 2 − √ tt 2 over t = 4 to t = 9 2. Compute the instantaneous acceleration for each velocity function at the indicated value of t. (a) v 1 (t) = t 3 + √ 3 t at t = 1 (b) v 2 (t) = 2 − 7 t at t = 3

(c) v 3 (t) = π + √ 31 t at t = π 3

  1. The figure below represents the position function of an electron moving through a certain magnetic field. (a) At what point in time does the electron return to its starting position? (b) What is the final position of the electron?

(c) At what time does the electron turn around?

2

Was this document helpful?

Math 11-Worksheet 06 - worksheet

Course: Calculus I (MATH 011)

81 Documents
Students shared 81 documents in this course

University: University of California, Merced

Was this document helpful?
Math 11 Worksheet 6 for Sections 3.3, 3.5, and 3.2b Spring 2023
1 Section 3.3
1. For each function, (i) compute the derivative and (ii) evaluate this at the given point.
(a) f(x) = (x2+ 1)(x−1), x =−1
(b) g(x) = (x3+ 2x−1)(x+ 2), x = 0
(c) h(x) = (x2−2x+ 3)(1 −3x+ 2x2), x = 1
2. For each function, (i) compute the derivative and (ii) evaluate this at the given point. You may use
the work done in previous problems, if applicable.
(a) f(x) = x2+ 1
x−1, x = 0
(b) g(x) = x3+ 2x−1
x+ 2 , x =−1
(c) h(x) = x2−2x+ 3
1−3x+ 2x2, x = 2
3. For each function, (i) compute the derivative and (ii) evaluate this at the given point. You may use
the work done in previous problems, if applicable. You need not simplify the results.
(a) f(x) = (x2+ 1)(x−1)2, x =−1
(b) g(x) = x(x3+ 2x−1)(x+ 2), x = 0
(c) h(x) = (x+ 1)(x2+ 3)
1−3x+ 2x2, x = 2
(d) r(x) = (x2−x+ 1)(−3 + 2x−x2)
x2+x, x = 1
4. Compute the derivatives of the following functions.
(a) B(x) = −x−11
(b) C(x) = x3/4
(c) D(t) = 1
t5
(d) E(x) = 3
√x
(e) F(x) = r1
x3
(f) H(x) = 5 5
√x4+1
x2
(g) I(t) = 3t5−5√t+7
t
(h) J(t) = t3/2(2 + √t)
(i) K(x) = x2+ 1
x
(j) L(θ) = θ−1
√θ
(k) M(x) = ax +b
c
(where a, b, c are constants)
1

Students also viewed

Related documents