Calculus

Video solutions

• انتگرال‌گیری با روش جایگزینی (u-substitution)
  Calculus · Calculus — Grade 12
  انتگرال زیر را با روش جایگزینی حل کنید:
  $$\int 2x \cdot e^{x^2}\, dx$$
• مشتق‌گیری با قانون ضرب
  Calculus · Calculus — Grade 11
  مشتق $f(x) = x^3 \sin(x)$ را پیدا کنید.
• Kinematics with Polynomial Position Functions
  Calculus · Calculus — University
  A particle moves along a straight line with position $s = (10t^2 + 20)$ mm. Find: (a) Displacement from $t = 1$ s to $t = 5$ s (b) Average velocity over that interval (c) Acceleration at $t = 1$ s
• Average Velocity, Average Speed, and Acceleration from a Position Function
  Calculus · Calculus — Grade 11
  A particle moves along a line with position $s = t^2 - 6t + 5$ (in meters), where $t$ is in seconds. Find the average velocity, average speed, and acceleration over the interval $0 \leq t \leq 6$ s, and the a…
• Position, Displacement, and Total Distance Using Derivatives
  Calculus · Calculus — University
  Given the position function $s = 1.5t^3 - 13.5t^2 + 22.5t$ ft, where $t$ is in seconds, find: 1. The position at $t = 6$ s 2. The total distance traveled from $t = 0$ to $t = 6$ s
• Velocity as a Function of Position Under Constant Acceleration
  Calculus · Calculus — University
  A particle travels along a straight line with constant acceleration. Given: when $s = 4$ ft, $v = 3$ ft/s; when $s = 10$ ft, $v = 8$ ft/s. Find $v$ as a function of $s$.
• Kinematics via Differentiation and Integration
  Calculus · Calculus — University
  Given: $v = (6t - 3t^2)$ m/s, $s = 0$ when $t = 0$. Find at $t = 3$ s: 1. Deceleration (acceleration) 2. Position $s$ 3. Total distance traveled 4. Average speed
• Kinematics with Calculus: Velocity, Acceleration, and Distance
  Calculus · Calculus — University
  A particle moves along a straight line with velocity $v = (12 - 3t^2)$ m/s. At $t = 1$ s, the position is $x = -10$ m (10 m to the left of the origin). Find: 1. The acceleration at $t = 4$ s 2. The displacement from t =…
• Kinematics: Position Under Constant Acceleration
  Calculus · Calculus — University
  A particle has an initial velocity of $v_0 = +12 \text{ ft/s}$ (to the right), an initial position of $s_0 = 0$, and a constant acceleration of $a = -2 \text{ ft/s}^2$ (to the left). Find the position $s$ of the particle…
• Calculus – Quadratic Equations Practice Set · 1
  Calculus · Calculus
  Question:
  Which of the following are the solutions to x squared minus 5x plus 6 equals zero?
  
  Calculus – Quadratic Equations Practice Set · 1
  
  This lesson demonstrates how to solve a quadratic equation of the form x^2 +…
• Calculus – Quadratic Equations Practice Set · 2
  Calculus · Calculus
  Question:
  Use the quadratic formula to solve 2 x squared minus 4 x minus 6 equals 0. Find both solutions.
  
  Calculus – Quadratic Equations Practice Set · 2
  
  This lesson demonstrates how to apply the quadratic formula to s…
• Calculus – Quadratic Equations Practice Set · 3
  Calculus · Calculus
  Question:
  Find all values of x satisfying x squared plus 4x plus 13 equals 0, expressing each root in the form a plus b i, where a and b are real numbers. Enter both roots separated by a comma.
  
  Calculus – Quadratic Equa…
• Calculus – Quadratic Equations Practice Set · 4
  Calculus · Calculus
  Question:
  A particle moves along a straight line so that its position at time t greater than or equal to 0 is given by s of t equals negative t squared plus 8t minus 7, in metres. At what time t does the particle first r…
• Calculus – Linear Equations Practice Set · 1
  Calculus · Calculus
  Question:
  Which of the following is the equation of the tangent line to f of x equals x squared plus 3x, at x equals 1?
  
  Calculus – Linear Equations Practice Set · 1
  
  This lesson demonstrates how to find the equation of …
• Calculus – Linear Equations Practice Set · 2
  Calculus · Calculus
  Question:
  Find the slope of the tangent line to g of x equals the square root of x, at x equals 9.
  
  Calculus – Linear Equations Practice Set · 2
  
  This lesson finds the slope of the tangent line to g(x) = √x at x = 9 usin…
• Calculus – Linear Equations Practice Set · 3
  Calculus · Calculus
  Question:
  The position of a particle is given by s of t equals t cubed minus 6t squared plus 9t plus 2. Find the equation of the tangent line to s of t at t equals 2.
  
  Calculus – Linear Equations Practice Set · 3
  
  This l…
• Calculus – Linear Equations Practice Set · 4
  Calculus · Calculus
  Question:
  Find the x-values at which the tangent line to h of x equals 2x cubed minus 12x is horizontal.
  
  Calculus – Linear Equations Practice Set · 4
  
  This lesson shows how to find the x-values where a polynomial curve …
• Calculus – Linear Equations Practice Set · 5
  Calculus · Calculus
  Question:
  Let f of x equal e to the 2x. The tangent line to f at x equals 0 intersects the x-axis at which point?
  
  Calculus – Linear Equations Practice Set · 5
  
  This lesson demonstrates how to find the equation of a tang…
• Solving Quadratic Equations with a Perfect Square Trinomial
  Calculus · Calculus
  Question:
  Solve: x squared plus 2x plus 1 equals 0.
  
  Solving Quadratic Equations with a Perfect Square Trinomial
  
  This lesson shows how to solve a quadratic equation whose left side is a perfect square trinomial. Student…
• Calculus – Factoring Polynomials Practice Set · 1
  Calculus · Calculus
  Question:
  Factor the polynomial p of x equals 6x cubed minus 9x squared minus 6x completely over the integers.
  
  Calculus – Factoring Polynomials Practice Set · 1
  
  This lesson walks through the complete factorization of a…
• Solving a Sum of Cubes Equation
  Calculus · Calculus
  Question:
  Solve for x: x cubed equals 30 cubed plus 40 cubed plus 50 cubed.
  
  Solving a Sum of Cubes Equation
  
  This lesson solves the equation x³ = 30³ + 40³ + 50³ by factoring out a common base and recognizing a perfect …

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