Urgent Assignment Help Needed: Struggling with Calculus Problems on Limits and Continuity

[henry110]

Hello everyone,
I hope you're all doing well. I'm currently working on a calculus assignment that's due soon, and I'm having a really tough time with a couple of problems related to limits and continuity. I've been stuck on these for hours and could really use some assignment help.

Here's one of the problems I'm struggling with:

1. Problem Statement:
   • Find the limit of the function 𝑓(𝑥)=2𝑥2−5𝑥+3𝑥−1f(x)=x−12x2−5x+3 as 𝑥x approaches 1.
   • Determine if the function 𝑓(𝑥)f(x) is continuous at 𝑥=1x=1.

My Attempt So Far:

• For finding the limit, I tried substituting 𝑥=1x=1 directly into the function, but it resulted in a division by zero.
• Then, I attempted to factor the numerator to see if I could cancel out the denominator, but I'm not sure if I'm doing it correctly.
• Regarding continuity, I understand that I need to check if the limit as 𝑥x approaches 1 is equal to the function value at 𝑥=1x=1, but given the division by zero issue, I'm confused about how to proceed.

Specific Questions:

1. What is the correct method to factor the numerator in this context?
2. How do I properly evaluate the limit without resulting in division by zero?
3. Once I find the limit, how can I determine if the function is continuous at 𝑥=1x=1?
4. Are there any online resources or textbooks that explain these concepts clearly for someone struggling with the basics?

I would be extremely grateful for any detailed explanations, step-by-step solutions, or pointers to relevant resources. I want to make sure I understand the process thoroughly so I can tackle similar problems on my own in the future.
Additionally, if anyone knows a reliable assignment writer who could offer professional assignment help, I'd appreciate any recommendations.

Thank you all in advance for your time and help!
Best regards,