Sajay Krishnan Paruthiyil

University of New Mexico
Teaching Assistantship

Biography

Currently employed as Teaching Assistant (Aug 2019 - May 2020) at University of New Mexico and expected to graduate in Nov 2020. Pursuing a Master of Science in Power and Energy emphasis under the department of Electrical Engineering.

Education

MS Electrical Engineering
University of New Mexico

Educator Statistics

Numerade tutor for 6 years
96 Students Helped

Topics Covered

Mastering Motion: Achieving Efficiency Along a Straight Line
Motion in 2d or 3d
Applications of Newton’s Laws
Mastering Integrals: Tips and Tricks for Calculus Success
Integration
Applications of Integration: Exploring Real-World Solutions
Unlocking the Power of Functions: Boost Your Programming Skills
Exploring the World of Derivatives: A Comprehensive Guide
Stand Out with Differentiation Strategies | Boost Your Business
Differential Equations Made Simple: Expert Tips & Resources
Mastering Integration Techniques for Optimal Results
Unlock the Power of Sequences: Boost Your Productivity
Discover the Best Series to Binge-Watch | Your Ultimate Guide
Mastering the Basics of Parametric Equations: A Comprehensive Guide
Polar Coordinates: Understanding the Basics and Applications

SAJAY KRISHNAN's Textbook Answer Videos

14:06
Calculus

For the functions in Exercises $39-46,$ find a formula for the Riemann sum obtained by dividing the interval $[a, b]$ into $n$ equal subintervals and using the right-hand endpoint for each $c_{k}$ . Then take a limit of these sums as $n \rightarrow \infty$ to calculate the area under the curve over $[a, b]$
$$f(x)=x^{2}-x^{3} \text { over the interval }[-1,0]$$

Chapter 5: Integration
Section 2: Sigma Notation and Limits of Finite Sums
Sajay Krishnan Paruthiyil
16:30
Calculus

Pumping water The rectangular tank shown here, with its top at ground level, is used to catch runoff water. Assume that the water weighs 62.4 $\mathrm{lb} / \mathrm{ft}^{3}$ .
a. How much work does it take to empty the tank by pumping the water back to ground level once the tank is full?
b. If the water is pumped to ground level with a (5/11) horsepower (hp) motor (work output 250 ft-lb/sec), how long will it take to empty the full tank (to the nearest minute)?
c. Show that the pump in part (b) will lower the water level lOft
(halfway) during the first 25 min of pumping.
d. The weight of water What are the answers to parts (a) and (b) in a location where water weighs 62.26 $\mathrm{lb} / \mathrm{ft}^{3} ? 62.59 \mathrm{lb} / \mathrm{ft}^{3} ?$

Chapter 6: Applications of Definite Integrals
Section 5: Work and Fluid Forces
Sajay Krishnan Paruthiyil
04:55
Calculus

In Exercises 35-38 :
a. Find $f^{-1}(x)$
b. Graph $f$ and $f^{-1}$ together.
c. Evaluate $d f / d x$ at $x=a$ and $d f^{-1} / d x$ at $x=f(a)$ to show that at these points $d f^{-1} / d x=1 /(d f / d x)$
$$f(x)=2 x+3, \quad a=-1$$

Chapter 7: Transcendental Functions
Section 1: Inverse Functions and Their Derivatives
Sajay Krishnan Paruthiyil
08:20
Calculus

a. Show that $f(x)=x^{3}$ and $g(x)=\sqrt[3]{x}$ are inverses of one another.
b. Graph $f$ and $g$ over an $x$ -interval large enough to show the graphs intersecting at $(1,1)$ and $(-1,-1)$ . Be sure the picture shows the required symmetry about the line $y=x$ .
c. Find the slopes of the tangents to the graphs of $f$ and $g$ at $(1,1)$ and $(-1,-1)$ (four tangents in all).
d. What lines are tangent to the curves at the origin?

Chapter 7: Transcendental Functions
Section 1: Inverse Functions and Their Derivatives
Sajay Krishnan Paruthiyil
09:22
Calculus

a. Show that $h(x)=x^{3} / 4$ and $k(x)=(4 x)^{1 / 3}$ are inverses of one another.
b. Graph $h$ and $k$ over an $x$ -interval large enough to show the graphs intersecting at $(2,2)$ and $(-2,-2) .$ Be sure the picture shows the required symmetry about the line $y=x$ .
c. Find the slopes of the tangents to the graphs of $h$ and $k$ at $(2,2)$ and $(-2,-2) .$
d. What lincs arc tangcnt to the curves at the origin?

Chapter 7: Transcendental Functions
Section 1: Inverse Functions and Their Derivatives
Sajay Krishnan Paruthiyil
08:20
Calculus

Tilted plate Calculate the fluid force on one side of a 5 ft by 5 ft square plate if the plate is at the bottom of a pool filled with water to a depth of 8 $\mathrm{ft}$ and
a. lying flat on its 5 ft by 5 ft face.
b. resting vertically on a 5 -ft edge.
c. resting on a 5 -ft edge and tilted at $45^{\circ}$ to the bottom of the pool.

Chapter 6: Applications of Definite Integrals
Section 5: Work and Fluid Forces
Sajay Krishnan Paruthiyil
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