1. T F If f is differentiable at a point a € D, then f must be continuous at this point. 2. TF If all partial derivative

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1 T F If F Is Differentiable At A Point A D Then F Must Be Continuous At This Point 2 Tf If All Partial Derivative 1 (39.07 KiB) Viewed 18 times

1. T F If f is differentiable at a point a € D, then f must be continuous at this point. 2. TF If all partial derivatives of f at a point a € D exist, then f must be differentiable at a. 3. TF Let X and Y be normed spaces. A bounded linear map L : X Y is uniformly continuous 4. T F A linear map L : RP → Rº maps unit vectors into unit vectors. 5. TF The function f(x) = ta is uniformly continuous on (1, ). 6. TF A positive definite matrix must be nonsingular. 7. TF If S : RP+R is smooth, then the graph of f is a smoothly parameterized p-surface. 8. TF The function f : R2 + R2: f(x,y) = (x,y) has a smooth inverse. 9. TF Let I: RP RP be the identity function. Then ||1|| = 1. 10. T F A px p matrix of rank p must have a nonzero determinant.