Limits & Continuity Problem Set (12 points): Be sure to look over the lecture, visit the “reading” website and watch the videos before beginning this problem set. You may use a graphing calculator. 6 problems, 2 points per problem for correct answers.
You must complete #1-2:
1) Where is f(x) discountinuous? Explain why.
![](data:image/png;base64,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)
2) Describe the intervals on which f(x) is discontinuous:
![](data:image/png;base64,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)
Choose any 4 of the following problems. Be sure to indicate on your answers which problems you choose.
Find the limit (if it exists).
3)
4) ![](data:image/png;base64,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)
5)
6) ![](data:image/png;base64,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)
(as x approaches – 3)
7)
8) ![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAF4AAAAlCAIAAABEVck7AAAFiklEQVRoge2Zf2wTZRjHn7NZ8VZs3dYau8TJ2oWSDEEpIEveGdDsh9kCGtt0QBgZJmqblEFEMFG7LOJ/xHiNspCQgMCRGEENbPE6iVGGFAsTYWRw4wqmJAM8es1K19n2yvlH17Vre6WDgjO5z3/3vs/zvs993+eee67FBEEAiVw88V8HMHuRpBFFkkYUSRpRJGlEkaQR5VFIEw+4PmxzXooXZDzBfN1e85Rm0cZDTGEOxSHQt9n82ZlA3i2FosOSlgaC5gu0Hv3p2GCYdzsMzQQTKX4wovActQVZezlxi1zSRCirEkBppSKCIAwTqNZK5Vkhg1uUFZlI3+T27m6EA4AaOX7Nt8TM1HwwwgxFWJEaoGHyDHi3o7aVoMNiDrmzJkJZlZPSzBCWNCktJMsLgiBwlMNOMnyYIdt1eHIwm3s3jtg6Sd8jTZkwQ7brwGDq7mVSUYQ8jhUGh1vsRIorDc+SFtzg8GTsxhAoezDBvdsDXY161GbtaNtx/O+Z7pcDhkBZkfM0sRKvtVK3MmwjlFUpFpgg5C/DNw6bKzFMb3Ndc9n0GKaqs33Qpi/FSld19R3tqtdgmKa+62QgZf/PdZqBFwzVsvSCd8b5kefV/fZlMgAIuGx6DNOscp4dObxRj+lt/ULt2z2u/Tvf//iLT1o0hRTQqMumwrDSVc7LIwfb9KUqmyt6H4/xP8gDv8Bd1zvVGLbA7DwzFbC8ZsEi2u3+S2SBnIKlsiZCWZU6K8UJwjCBlDjqdnPXSZMWdO0kE2JJCz7tiHykSTttIFG2AEBnp7jE6YRpohmvMiB7vhKYH54mVuJaHdqWXDONHFkzTCC1znKA4cM00YynP9osacJ1YpV0Ri9vhdFsXlGmqtDgUGl8Wa9QVpSXTDMI3bkV02pUqaSRN+0eCzO929DNI3t/HAUAAFxft7zKV2XubCgT2yeRGBnUO73JeZl++StVsUrzpqYyWaZLTeepYE/znDSXqO/KRWVTR6tehs9ft6EFzp4aDE56KSs0JVm7Jyl6X1OiqVDJpo3g+pZNZiOevIwHuUAMLg38flt0DXnT7rGsQxzYrJ8yCPrZ2PjgwPk72S7pWZNwkVctWBT8+TQdh4QWZZpyeSF3Ii5NjPMH4xD0s7EJ1h+C+JifHWf9Y2lNUjzo52IJszS36TYAAHHvudNs3ZuNlQAAAapr35y1a0qGaGbkxEnvg7R5t11d35WvfQ2GaGbk5AnvxP3s5zWbl/oO9XzjDXiPHHZpW1qXKAraJ8dDxhAoMYc63kOJUrEQIS0AAGgRqgUAAKURGZWTZgQz6Tmt1vAehwEAAHBkP+BhBSHCEA2ANxN0iCUteNWLlq+GZtzKMAQC9UpiiGdJE641WPZkdkO53lACz/TaEQ4AOgvhYVPjeWtNcbvhkMdhxE0ke3/L2QFDoKkOMIvi1ponqw01MERff5xfQw9BlLly0VBXNy936Xl4aUIXdq1udF4GAACZunF1y036av7PttnC+IXT57WW15fIck9nSSNww71H+72st7/vLMenxuOXdm/dO5J5y0L0z/27vr2WqoTqNdu3cN/3jxYj9EcNd5V+3rZ+sYgy2dJgc59VnNte37bnSiAQiKXGZQvftUYdW/sC6cbRwS8Plnasq04bUizb0qk9djxLxNlGPOD6vKd8w4b5uKhJjvrDkia1lYpEGKIhy9zoOLQTTV0plj43VwYAUPLGvtFY0p/nqB0WYuZvn8cJ12s37XRnN9NpZEoT++3TusVvrV/zEtr6g+9e2gTPUN07CE8oa4UIQ7QiYrgY8c4uMCHjLzphYjwsL4W7YyWqp+VYIakpjN9hoewZhdgz+38lSxqJJNLP5qJI0ogiSSOKJI0okjSiSNKIIkkjiiSNKJI0okjSiPIv1lQCbt27Ld0AAAAASUVORK5CYII=)
(as x approaches – 4)
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