TEST 20
1.
\(F(x,y)=\ln(x-y)+2y-x^2+2=0\)
\(\Rightarrow F'(2,1)=?\)
A) \(-3\)B) \(0\)C) \(\samefrac{1}{2}\)D) \(1\)E) \(3\)
2.
\(F(x,y)=\sin x+\cos y=0\)
\(\Rightarrow F'\left(0,\samefrac{\pi}{2}\right)=?\)
A) \(-1\)B) \(-\samefrac{1}{2}\)C) \(0\)D) \(\samefrac{1}{2}\)E) \(1\)
3.
\(2x^2-2y=\sin(x+y)\)
\(\Rightarrow\left.\samefrac{dy}{dx}\right|_{\substack{x=0\\y=\pi}}=?\)
A) \(-1\)B) \(-\samefrac{1}{2}\)C) \(0\)D) \(\samefrac{1}{2}\)E) \(1\)
4.
\(\tan(x+y)=x+y\)
\(\Rightarrow\samefrac{dy}{dx}=?\)
A) \(\samefrac{\sin^2(x-y)}{1+\cos(x-y)}\)B) \(\samefrac{\sin(x-y)}{\cos^2(x-y)+1}\)C) \(\samefrac{\sin^2(x-y)}{1+\cos^2(x-y)}\)D) \(1\)E) \(-1\)
5.
\(F(x,y)=y+x\cdot\cos y+y\cdot\sin x-\samefrac{\pi}{2}=0\)
\(\Rightarrow F'\left(0,\samefrac{\pi}{2}\right)=?\)
A) \(-\samefrac{1}{2}\)B) \(\samefrac{1}{2}\)C) \(\samefrac{1}{3}\)D) \(-\samefrac{\pi}{2}\)E) \(\samefrac{\pi}{2}\)
6.
\(F(x,y)=\tan^2x-\tan(x+y)=0\)
\(\Rightarrow F'\left(\samefrac{\pi}{4},0\right)=?\)
A) \(-2\)B) \(-1\)C) \(0\)D) \(1\)E) \(3\)
7.
\(F(x,y)=x^3+y^3-xy-1=0\)
\(\Rightarrow F'(1,0)=?\)
A) \(-3\)B) \(-\samefrac{1}{3}\)C) \(\samefrac{1}{3}\)D) \(\samefrac{2}{3}\)E) \(3\)
8.
\(F(x,y)=\sin x-\tan y+k=0\)
\(\Rightarrow F'\left(\samefrac{\pi}{3},\samefrac{\pi}{4}\right)=?\)
A) \(-\samefrac{1}{4}\)B) \(-\samefrac{1}{2}\)C) \(\samefrac{1}{4}\)D) \(2\)E) \(4\)