Watch comprehensive video reviews for most units, designed for final exam preparation. Each video includes integrated problems you can solve alongside detailed solutions.
Not your average video:
Interactive Problems: Solve problems alongside the video with step-by-step guidance and detailed solutions.
Exam Preparation: Complete unit reviews designed for final exam preparation with all key concepts covered systematically.
Expert Teaching: High-quality instruction from Perplex co-founder James Mullen with clear explanations, worked examples, and exam tips.
Not your average video:
Interactive Problems: Solve problems alongside the video with step-by-step guidance and detailed solutions.
Exam Preparation: Complete unit reviews designed for final exam preparation with all key concepts covered systematically.
Expert Teaching: High-quality instruction from Perplex co-founder James Mullen with clear explanations, worked examples, and exam tips.
Proof and Reasoning
Watch comprehensive video reviews for Proof and Reasoning, designed for final exam preparation. Each video includes integrated problems you can solve alongside detailed solutions.
Not your average video:
Interactive Problems: Solve problems alongside the video with step-by-step guidance and detailed solutions.
Exam Preparation: Complete unit reviews designed for final exam preparation with all key concepts covered systematically.
Expert Teaching: High-quality instruction from Perplex co-founder James Mullen with clear explanations, worked examples, and exam tips.
Not your average video:
Interactive Problems: Solve problems alongside the video with step-by-step guidance and detailed solutions.
Exam Preparation: Complete unit reviews designed for final exam preparation with all key concepts covered systematically.
Expert Teaching: High-quality instruction from Perplex co-founder James Mullen with clear explanations, worked examples, and exam tips.
The video will automatically pause when it reaches a problem.
AHL AA 1.15
Let f(x)=eax. Prove that
for all integers n≥0.
Let P(n) be the proposition that
Verify P(0):
Assume P(k) is true:
Show that P(k+1) is true:
Thus, P(k+1) is true.
Conclusion:
Since P(0) is true and if P(k) is true then P(k+1) is true, P(n) is true for all integers n≥0.
AHL AA 1.15
Let f(x)=eax. Prove that
for all integers n≥0.
Let P(n) be the proposition that
Verify P(0):
Assume P(k) is true:
Show that P(k+1) is true:
Thus, P(k+1) is true.
Conclusion:
Since P(0) is true and if P(k) is true then P(k+1) is true, P(n) is true for all integers n≥0.