Instructors
Dr. Raphael Bahati
CEO & FounderE-mail: rbahati@bahatiacademy.com
“Elementary techniques of integration; applications of Calculus such as area, volume, probability; functions of several variables, Lagrange multipliers. This course is intended primarily for students in the Social Sciences, but may meet minimum requirements for some Biological or Basic Medical Sciences modules. It may not be used as a prerequisite for any Calculus course numbered 1300 or above.”
Q: \(f(x) = \begin{cases} 3x^2, & \text{if }x \leq -1 \\ 1 - 2x, & \text{if }-1 < x < 0 \\ x + 2, & \text{if }x \geq 0\end{cases}\). Find \(\displaystyle \lim_{x \to 0^+} f(x)\) if it exists. (a) \(4\) (b) \(1\) (c) \(DNE\) (d) \(3\) (e) \(2\)
“Introduction to differential calculus including limits, continuity, definition of derivative, rules for differentiation, implicit differentiation, velocity, acceleration, related rates, maxima and minima, exponential functions, logarithmic functions, differentiation of exponential and logarithmic functions, curve sketching.”
Q: Find \(\displaystyle \int \dfrac{4x^3 - 2}{x^4 - 2x + 1}\, dx \) (a) \((x^4 -2x)\ln|x^4 - 2x + 1| + C\) (b) \( \ln|x^4 - 2x + 1| + C\) (c) \(\dfrac{x^4 - 2x}{\frac{1}{5}x^5 - x^2 + x} + C\) (d) \( \ln|\frac{1}{5}x^5 - x^2 + x| + C\) (e) \(4\ln|x| - \ln|x - 1| + C\)
“Permutations and combinations; probability theory. This course is intended primarily for students in the Social Sciences, but may meet minimum requirements for some Biological or Basic Medical Sciences modules.”
Q: Let the universal set be \(U = \{1, 2, 3, 4, 5, 6, 7, 8\}\). If \(F = \{1, 3, 6, 8\}\) and \(G = \{2, 3, 6, 8\}\).
Find \(F \cap G\).(a) \(\{3, 6, 8\}\) (b) \(\{1, 2, 4\}\) (c) \(\{1, 2, 4, 5\}\) (d) \(\{1, 4, 5\}\) (e) \(\{ 1 \}\)
“Matrix algebra including vectors and matrices, linear equations, determinants. This course is intended primarily for students in the Social Sciences, but may meet minimum requirements for some Biological or Basic Medical Sciences modules. ”
Q: Let \(\left[\begin{array}{ccc|c}1&0&3&1\\0&1&0&1\end{array}\right]\) be the argumented matrix for a system of linear equations. The solution to this system of equations is: (a) \((0, t, 3)\) (b) \((1 + 3t, 1, t)\) (c) \((1 - 3t, 1, t)\) (d) \((1- 3t, 0, t)\) (e) \((1 - 3t, t, 1)\)
“Properties and applications of vectors; matrix algebra; solving systems of linear equations; determinants; vector spaces; orthogonality; eigenvalues and eigenvectors.”
“Review of limits and derivatives of exponential, logarithmic and rational functions. Trigonometric functions and their inverses. The derivatives of the trig functions and their inverses. L'Hospital's rules. The definite integral. Fundamental theorem of Calculus. Simple substitution. Applications including areas of regions and volumes of solids of revolution.”
“Integration by parts, partial fractions, geometric series, harmonic series, Taylor series with applications, arc length of parametric and polar curves, first order linear and separable differential equations with applications. ”
“This course should be taken by students who intend to pursue a degree in Actuarial Science, Applied Mathematics, Astronomy, Mathematics, Physics, or Statistics. The course will cover: The Mean Value Theorem and its consequences; Techniques of integration; Series; Taylor series with applications; Parametric and polar curves with applications; First order linear and separable differential equations with applications. ”
E-mail: rbahati@bahatiacademy.com
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