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1. Indicate whether the following statements are true or false. No justification necessary. (a) Suppose 7 (t) is a vector-valued function having well-defined Frenet frame {T (t), N(t), B (t)} Then we must have B(t) × N(t) = T (t) at all times t. TRUE FALSE (b) Suppose 7 (t) is a vector-valued function having well-defined Frenet frame {T (t), Ñ(t), B (t)} (same as above). Then we must have B(t) x T (t) = N(t) at all times t. TRUE FALSE (c) * > 0 everywhere as well. Then we must have f(4,1) > f(2,1). Suppose a function f(x, y) is differentiable everywhere, and suppose further that Əx TRUE FALSE (d) af Suppose a function f(x, y) is differentiable everywhere, and suppose further that > 0 everywhere as well (same as above). Then we must have f(4, 3) > f(2,1). TRUE FALSE (e) intersects the graph z = f(x, y) at P and only at P. Given a function f(x,y) and a point P in the domain, the tangent plane Tpf TRUE FALSE

1. Indicate whether the following statements are true or false. No justification necessary. (a) Suppose 7 (t) is a vector-valued function having well-defined Frenet frame {T (t), N(t), B (t)} Then we must have B(t) × N(t) = T (t) at all times t. TRUE FALSE (b) Suppose 7 (t) is a vector-valued function having well-defined Frenet frame {T (t), Ñ(t), B (t)} (same as above). Then we must have B(t) x T (t) = N(t) at all times t. TRUE FALSE (c) * > 0 everywhere as well. Then we must have f(4,1) > f(2,1). Suppose a function f(x, y) is differentiable everywhere, and suppose further that Əx TRUE FALSE (d) af Suppose a function f(x, y) is differentiable everywhere, and suppose further that > 0 everywhere as well (same as above). Then we must have f(4, 3) > f(2,1). TRUE FALSE (e) intersects the graph z = f(x, y) at P and only at P. Given a function f(x,y) and a point P in the domain, the tangent plane Tpf TRUE FALSE

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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need problems C), D), E)

multivariable calculus

1. Indicate whether the following statements are true or false. No justification necessary. (a) Suppose T (t) is a vector-valued function having well-defined Frenet frame {T (t), N(t), B (t)}. Then we must have B(t) x N (t) = T (t) at all times t. TRUE FALSE (b) Suppose T (t) is a vector-valued function having well-defined Frenet frame {T (t), N (t), B (t)} (same as above). Then we must have B(t) × T (t) = N(t) at all times t. TRUE FALSE (c) af Suppose a function f(x, y) is differentiable everywhere, and suppose further that > 0 everywhere as well. Then we must have f(4, 1) > f(2, 1). TRUE FALSE (d) Suppose a function f(x, y) is differentiable everywhere, and suppose further that > 0 everywhere as well (same as above). Then we must have f(4,3) > f(2,1). TRUE FALSE (e) intersects the graph z = f(x, y) at P and only at P. Given a function f(x, y) and a point P in the domain, the tangent plane Tpf 8 TRUE FALSE
Transcribed Image Text:1. Indicate whether the following statements are true or false. No justification necessary. (a) Suppose T (t) is a vector-valued function having well-defined Frenet frame {T (t), N(t), B (t)}. Then we must have B(t) x N (t) = T (t) at all times t. TRUE FALSE (b) Suppose T (t) is a vector-valued function having well-defined Frenet frame {T (t), N (t), B (t)} (same as above). Then we must have B(t) × T (t) = N(t) at all times t. TRUE FALSE (c) af Suppose a function f(x, y) is differentiable everywhere, and suppose further that > 0 everywhere as well. Then we must have f(4, 1) > f(2, 1). TRUE FALSE (d) Suppose a function f(x, y) is differentiable everywhere, and suppose further that > 0 everywhere as well (same as above). Then we must have f(4,3) > f(2,1). TRUE FALSE (e) intersects the graph z = f(x, y) at P and only at P. Given a function f(x, y) and a point P in the domain, the tangent plane Tpf 8 TRUE FALSE
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